Mechanisms for seasonal color change
This was an interesting question, and I did a little research. It's remarkable how many different mammals and birds do this, so it must be amazingly useful as a survival mechanism.
This Powerpoint paper on weasels seems to show that the amount of light has something to do with the change mechanism, with melatonin a factor, which is logical. Humans also changed color over time with the enviroment, although Vitamin D seems to have been a primary driver there.
Remember, odds are good that the genes for all the different coat colors were already in place.