Is "dark clothes for winter, light for summer" relevant? We are told to wear light clothes in summer as they are better at reflecting sunshine and keeping us cool. And dark clothes absorb sunshine and keep us warm.
But is it really relavent? If I buy identical t-shirts, one in black and one in white, will I feel significantly cooler or warmer? I have noticed that black surfaces get much warmer, but do they make the person warmer too?
 A: This article has some relevant results based on a study of bird plumage (it also happens to be cited in the abstract of the Nature paper mentioned in one of the other answers), and is summarized in simpler terms here.
I'll attempt to summarize the summary.
Black and fluffy/loose fitting clothing is best if it is hot out and there is any ($>3 \mathrm{m}/\mathrm{s}$) wind. The black clothing absorbs both solar radiation and radiation from the body. The air in the immediate vicinity is heated, then efficiently transported away by the wind. This is slightly better than white fluffy/loose fitting clothing, which reflects more sunlight and radiation from the body. The emission from the body is reflected, so it cannot heat the air near the clothing as efficiently and have a chance to be transported away.
Tight black clothing is a terrible idea if trying to stay cool, regardless of windspeed.
If there is no wind ($<3 \mathrm{m}/\mathrm{s}$), white clothing is better since the most important thing in these conditions is to reflect as much incoming sunlight as possible.
I also have another possibility to think about. My recollection regarding loose fitting black robes in the desert is that - given a garment that is open at the bottom (robe) and top (not too tight fitting) - heating the air inside is actually advantageous to keeping cool since this drives a convection flow upward through the garment. This airflow makes cooling via sweating efficient, enough that the person wearing the garment doesn't feel as hot. Unfortunately I can't find any experimental results to validate this picture, but it seems more or less in line with the results above, at least in as much as airflow seems to be key to answering the question.
A: For most circumstances this is a myth and the opposite is more true.
If you are standing in direct sunlight it would best best to wear white clothes to reflect the heat. The direct radiation from the sun would have a temperature higher than your body so it would absorb heat. A black surface can heat up to over 40 degrees in direct sunlight.
However, if you are standing in the shade on a hot day where temperature is less than body temperature of 37 degrees Centigrade, then black clothes may well radiate more heat away than they absorb from ambient heat. For most of the time black clothes will therefore be better in the heat.
In cold weather you will want to keep heat in so it would be better to have white clothes that reflect heat on the inside and radiate less on the outside. This would be true because the ambient temperature is going to be well under body temperature. Emergency survival blankets are silver on both sides to keep heat in.
A: I wouldn't say it is a myth. Like you say, it's complicated. When you are in the sun, the predominant source of heating is from incident radiation, whereas in the shade cooling would take place primarily through convection, conduction and evaporation. When you are in the shade, you are just not that hot compared to your surroundings for radiative cooling to be very effective (10 degree difference).
If you stay in the deep shade all summer, by all means, wear whatever colour you like. But don't go hiking with a black shirt on.
In the winter, where body temperature might be 45 degrees from ambient, radiation will play a big role. Of course, if you're well insulated then your overall surface temperature is close to ambient, and the effect may be negligible (e.g. a white parka and a black parka may perform similarly).
A: There are physical and physiological aspects of this problem. Consider this: if your fingers are freezing in cold is it better to drink a hot tea or cold vodka? Definitely VODKA! Why? because it will immediately cause your blood vessels to widen, more blood will go to your fingers and you'll have a better chance to save them. Did I make this up? No. My cousin went to a nurse school, and I read this in her first aid textbook many years ago. 
Hence, we have to consider the physiological aspect here. If in a cold whether your clothes are cold, then your skin will feel cold, and that will shot down the blood supply to the skin, you'll feel colder. If you're wearing dark t-shirt it must get warmer because it will absorb more energy from Sun than a white t-shirt, so the blood supply should be better, and you'll feel warmer. That is assuming there is Sun, i.e. maybe late Spring or early Fall.
If this is Russian winter, then you're not going to be wearing a t-shirt. You'll be wearing a fur coat. It works differently. It works through conservation of heat. Its heat transfer is very low. Even if Sun warms it outside, that heat is not going inside. Your body's heat is not going outside either. Hence the color of a fur coat doesn't matter, it can be white or black, no difference. here's the proof:

A: Although counterintuitive, inhabitants of the desert often wear black. In fact, studies show that the color of their clothes make no difference to the heat gained. See e.g. this article in Nature.
Though this assumes that their robes are loose-fitting, such that convection is relevant.
A: First of all, there is no passive material that passes thermal radiation in one direction better than in the other.
The best material for thermal isolation is highly reflective (e.g. aluminum foil). Ideally, this does not emit any thermal radiation. (It also does not absorb thermal radiation, hence, it is an isolation).
The worst is black because that radiates thermally. It also absorbs thermal radiation, but if you want isolation, this is worst.
So best clothes for winter and summer would be highly reflective (Provided you want thermal isolation from the cold in winter and from the hot in summer).
But keep in mind that heat transport is not only by radiation, but also by heat convection and heat conduction. 
