What is cold wind? As per my understanding, temperature is the movement of particles in an environment. A highly energetic environment where particles possess high energy has a high temperature,
and low energy means low temperature.
Wind in general means speed and energy in my opinion, so what does cold wind mean? How can it exist?
Is it a bunch of super stable particles moving together?
Does it move slowly? Air conditioning transfers heat okay, but what happens at the particle level? Do particles suddenly stop moving/less movement when they hit the heat transferring element-how?
 A: There are already two amazing answers above, but I think explaining it more simply might be helpful:

*

*Molecules in wind have vibrational motion as well as translational motion.


*The vibrational speed is higher than the translational speed(in general situations).


*The more the vibrational speed, more is the kinetic energy in the molecules, hence more the heat content and temperature of the wind.


*So the temperature depends on the vibrational motion and not the translational motion, the latter which we feel as blowing wind, and we feel the vibrational motion as heat. The translational motion is independent of vibrational motion in the wind molecules.


*If the vibrational speed is more than the vibrational speed of molecules in our skin, we feel warmer as heat travels from wind to our skin, and the other way round for the opposite.
A: Technically, it all is the same motion. The difference is magnitude and direction and how you separate out the superposition of them.
Temperature is a result of the components of motion (vectors) of each individual air molecule with a net translational movement of zero over time. This motion is random and all over the place in many directions as they move around, collide and bounce off each other and objects. This speed is apparently around 500m/s, just to give you an idea:
https://pages.mtu.edu/~suits/SpeedofSound.html
Wind is the collective motion of a mass of randomly moving air molecules: the average velocity of the actual motion of the individual air molecules. Averaging their velocities cancels out the vectors that point in "random" directions which lead to net zero motion, leaving only the collective translational motion remaining. Obviously, wind is usually not 500m/s.
So, typically, the random net-zero impact vectors between air molecules and objects are much higher speed than those due to the collective/average motion of the air molecules (wind). This means the net-zero impact vectors dominate over the translational impact vectors in kinetic energy transfer (heat) in either direction into or out of your body.
But if you're an SR-71 flying through the air at Mach 3, the relative wind speed is so high that the vectors of the translational motion of the air molecules is much larger than that of the net zero, random motion.  The result is a net heating of the aircraft skin due to impacts from the wind even if the random velocities of the individual air molecules make for very cold air that would otherwise cool down the airplane's skin.
So a cold wind would be one where the kinetic vibratory motion (thermal motion) of the molecules in your body is higher than the random motion of the individual air molecules such that energy is transferred out of your body into the air from the collisions   rather than into it, and impacts vectors for the average motion of the air (wind) is too slow to to transfer energy from the air into your body and only replaces the air molecules heated up by your body with fresh, cold air molecules.
A: Temperature is related to motion, yes. And wind is motion. But numbers matter.
A particle with temperature $T$ (in absolute units, like Kelvin) will typically have a kinetic energy of approximately $kT$, where $k$ is Boltzmann’s constant. For nitrogen and oxygen molecules at room temperature, the typical speed associated with this typical kinetic energy is a few hundred meters per second. That’s an order of magnitude faster than the winds in Earth’s fastest storms. Thermal motion is closer to the speed of sound than the speed of wind. (Why is the speed of sound close to the mean thermal speed? That’s a fun question to try and figure out on your own.)
We don’t ordinarily care very much about the speeds of individual molecules in the air, because their mean free path is very short: less than 100 nanometers for air at room temperature. Even though those molecules are zooming around, they never go very far before they change direction.
If I light a match across the room from you, you’ll hear the noise within milliseconds, because the pressure wave to which your ear responds travels at approximately the mean thermal speed.  But you might not smell the smoke from the match for many seconds, because the smelly molecules to which your nose responds have to make their way over to you by diffusion.
A “wind” is collective motion of all the molecules in the gas. Each molecule in the wind has a thermal motion whose direction is almost random, with only a slight preference for the downwind direction. Because the thermal motion is so much faster than the wind speed, there is plenty of room for the temperature of the collectively-moving air to be lower than the temperature of the collectively-stationary air which it is displacing.
