I came of age around 1983 and studied the issue, so I remember how it was all supposed to unfold.
The most visible part of a nuclear explosion is the initial flash, nicknamed the Pika, which is like a massive strobe of a few hundred milliseconds duration. The strength of the Pika is dependent on the size of the bomb. Most US weapons were in the sub megaton range usually under 500kt while most Soviet weapons were in the megaton range.
The fireball and mushroom clouds would not be particularly visible beyond low earth orbit although the great clouds of debris and smoke from firestorms in cities and woodlands would eventually blanket most of the earth and be visible from out to the moon. Detonation in orbit, undimmed by the earths atmosphere would be visible from Mars and beyond without a doubt.
The actual pattern of Pika flashes would depend on how closely the real world followed doctrine. It is unlikely that a real nuclear attack would unfold in the clockwork fashion depicted in movies and fiction. In reality, the Soviet Union in 1983 was a disintegration mess and in any case, flawless precision in timing has never been a Russian strength. Brutal frontal assaults are their forte.
If the Soviets in their psychotic ideological driven paranoia had actually pushed the button, the actual war have been a relatively slow-motion cluster-f*ck of epic proportions with a lot of missiles blowing up in silos and subs and vast number of units double and triple checking the actual order to fire and many never firing at all.
An unknown number of Soviet military personnel would likely simply refused to carry out their orders. Russia, as a land empire, has always had a political culture in of deep mistrust of fellow citizens and the state. Even in a totalitarian state were KGB commissars could shoot men out right for disobeying orders, and where those responsible for launching nuclear weapons were chosen first for their political reliability, there were plenty of brave men who would rather stand and die than risk starting a nuclear war by mistake. Indeed, on at least two occasions, solitary Soviet officers stopped possible nuclear launches.
That combination of equipment failure and human hesitation would likely make a nuclear strike a ragged affair with weapons detonating in fairly small numbers at first in seemingly pointless pattern drawn out many more hours than originally planned.
There was also the issue of nuclear friendly fratricide in which one weapon detonating destroyed other weapons from the same side. In fact, one plan for deploying the Minute Man III was the dense pack system in which the silos were packed side by side like beer cars in a case. The first Soviet detonation would raise such a debris cloud that it would destroy all further incoming Soviet warheads but the Minute Man missiles could still pass up through the cloud at launch speed.
However, if the Soviet attack had unfolded as planned it would appear from space something as follows
00:00 Soviet doctrine sought surprise and maximum destruction of both civilian and military targets. If they could time the strike, they hit sometime around 0400 Eastern standard time in North America.
00:00- The Walker spy ring had provided the Soviets with the ability to decrypt US Naval submarine communications so it's likely their very first targets would be US Naval ballistic subs attacked with tactical nuclear torpedoes launched from Soviet attack subs and aircraft. From obit, these attacks would look like large lighting flashes followed by outsized mushroom clouds of steam. Radial shockwaves across the ocean surface would be visible.
Since many US subs ran "dark" at depth never communicating their exact position and US subs usually knew if Soviet subs were nearby in any case. The Soviets wouldn't have gotten them all.
00:00 - The next Soviet targets would the political centers and military command and control (C&C) of all the other nuclear powers. A key observer in low earth orbit, roughly 90 miles, passing overhead with clear weather at night might see small bright sparks arise from the night dark ocean around 300 miles off the east and west cost of North America.
00:05, The first multi-megaton flashes would appear over Washington, D.C., London, Paris and Beijing as several sub-launched missile warheads detonated carpet bomb fashion over the cities. The Soviets would attempt a decapitation strike, killing the civilian leadership of the other nuclear powers in attempt to delay counter launches.
From low earth obit, 90 miles straight up, the Pika would look like a blinding flash of lighting and would temporally blind the astronaut.
00:05-00:10 The Soviets didn't have enough subs to attack all the other nuclear powers, so they would concentrate all subsequent fire on North America. The whole costal areas of the North America, would erupt with flashes every 15-20 seconds for around 5 minutes. From the moon, it would look like overly bright camera flashes in a crowd in a sports stadium.
Soviet subs would also attack some US military bases around the world at the same time so flashes would erupt on islands like Guam and costal areas in the middle-east, pacific and Japan.
The mushroom clouds from the very first attacks by now have risen far above the natural cloud layer. They would appear as thin cylinders of smoke until they struck the jet stream then they would spread out in near perfectly flat smear headed downwind. They would not be visible from the moon.
00:5-00:10 tactical missiles from Eastern Europe and Mongolia would strike West Germany, Northern China and South Korea. These would be tiny pin prick flashes in comparison but there would be a lot more of them.
00:15, There would be a pause for about 5-10 minutes for the flight times of land based ICBMs then huge flashes (blinding from orbit) would start in West Germany, Finland Sweden and Switzerland and then walk Westward over the course of the next 5 minutes until they stopped in Ireland. At the same time, a similar pattern of flashes would walk north to south across China and Korea. After a 2-3 minute pause, the flashes would walk across Japan.
00:15-00:20 Eastern Europe erupts in pin pricks as surviving Nato tactical weapons retaliate. Around this time, 15 minutes after the start of the war, anyone in low earth orbit would see mushroom clouds rising over American costal cities. Then, Soviet anti-ballistic missile warheads launched from a facility just over Moscow would saturate low orbits to try and intercept incoming US warheads. Anyone in low earth orbit over the northern hemisphere is now likely dead. (That's assuming they weren't targeted by Soviet anti-satellite nukes at the outset.) An observer on the moon would be blinded by these flashes and they would visible from the surface of Mars as clusters of distinct flashes.
00:15-00:20 Cuba disappears under a saturation of flashes. Japanese and South Korea cities erupt in multi-megaton flashes again. This time, its warheads from China.
Small flashes occur over the seas as ships and submarines are engaged.
00:15-00:20 Costal areas of the Soviet Union flash as US submarine launched missiles find their targets. These flashes are in the sub 500kt range and land almost simultaneously within a couple of hundred feet of hard military targets. From LEO, these flashes look coordinated and patterned, like bulbs in a marque sign flashing suddenly. From the moon, it looks like the territory of the Soviet Union is rimmed with strobes.
00:15-00:20 Most major Soviet cities flash from multi-megaton Chinese land based ICBMs.
00:30-0045 Warheads from Soviet land based ICBM flash over Canadian cities and military bases and gradually walk southward over American cities over the next 15 minute going as far south as Mexico city.
00:40-00:55, the Soviet interior erupts in tight clusters of multiple simultaneous flashes as US Minute Men missiles precision carpet bomb Soviet silos and bases deep in the Soviet interior.
01:00 Small flashes over Europe and northern Asia as surviving fighters and air defenses engage incoming Soviet bombers with small kiloton sized anti-aircraft missiles. Flashes visible from LEO and faintly from the moon.
02:00-03:00 Soviet ship launched cruise missiles strike major cities in South Africa, Australia and New Zealand. Multi-megaton flashes easily visible from the moon
06:00-0800 US bombers reach the Soviet union and another battle of small pika erupts around the Soviet perimeter. Then slowly, over the course of the next 3-6 hours. Bright flashes erupt as US bombers drop multimegaton warheads on Soviet mobile missile batteries and deeply buried command and control centers. No Soviet bombers reach North America but they do sweep across the mid-east and India striking major cities.
12:00 All flashes stop. From the moon, the day lit areas of the Northern hemisphere appear shrouded in grey clouds. On the night side, the clouds glow a faint orange color and through any breaks, an observer on the moon can see vast fires burning in cities and spreading to wild lands.
24:00+ the entire northern hemisphere land mass and much of the sees are blanketed for a solid mass of dirty grey clouds and nothing can be seen.
72:00+ Surviving US and Soviet deep boomers rise to communication depth and attempt to contact C&C. Depending on what C&C survived and what they believe necessary, the submarines may launch another wave of attacks. Missile silos and mobile batteries that survived the first round may join in.
This time the flashes look like heat lighting under the thick sheet of smoky clouds. Visible form orbit, faintly so from the moon. Slowly it all peters out.
After a few weeks at most, the clouds would dissipate (screw you Carl Sagan and your self-lofting cloud.) An observer from the moon would see vast areas of grey and black from vast fires that covered millions of acres. Many would still be burning as plants dying of radiation from fallout dry out and catch fire.
From LEO, the great rivers of the world turn black as rain washes Terratons of soot from the land and sky down the watersheds. Over the next few months, the worlds river outflows in the sea are visible as spreading black tendrils slowly dissipating.
Long term, the appearance of the Earth is uncertain. Only Central Africa and perhaps parts of South America would still appear green. The northern hemisphere is largely black of fires and the grey of dead vegetation. At first, massive fires and decaying vegetation would release huge amounts of greenhouses gasses so that for a 2-3 years afterwards, the climate might be unusually warm. On the other hand, the death of vast swaths of vegetation would increase the earths albedo and heat retention so it might balance out producing little net change.
The best hope for humanity would be that US intelligence would have detected the signals of the Soviet preparing to attack and that Reagan would have tired a pre-emptive attack. If the faint hope of American military planners that relatively small, precise nuclear strikes could cripple the Soviets ability to launch were born out, most of humanity would have survived. American first strike weapons were relative small and configured for minimal fallout and targeted away from Soviet cities (except Moscow.) Around 70% of the Soviet population would have survived the first strike. If China never launched, the war would have been over within an hour.
Coincidentally, in 1983, my senior year in High School I had a horrific nightmare about living in the after effects of a nuclear war. I was a science geek so I knew all the details.
I lived in rural Texas far from any immediate targets and would have survived for at least weeks or months after the war. In the dream, my grandmother and I, sole survivors of our family. struggled to save our live stock and ourselves from starvation and the ravages of radiation poisoning.
It was the most realistic and immersive dream I ever had, I felt, I really felt, the pain of knowing that all I knew and loved were dead. I remember how my grandfather, put us down in the storm shelter and then staid outside to add shielding and arraign supplies. I remembered in the dream how he was still alive two weeks later when my grandmother and I cam out of the shelter. I remembered in the dream how he died slowly and horribly a week later, virtually rotting alive.
I awoke gasping and crying and for the next two days this cowboy boot wearing. Bull riding touch Texas farm boy would break down weep at the memory of horror of that dream. Sometimes, I still do. When I saw the Battlestar Galactic reboot mini-series, it was the first time in my life I can remember seeing a depiction of planet wide nuclear attack. I almost broke down again.
Had my dream been real, the slow deaths of myself and my family would not have been visible from orbit.