I was told that the Winter White dwarf hamster changes color based on the season. i.e. brown/dark grey in the summer and white/light grey in the winter. Firstly, what causes the hamster to notice the shift in seasons? Is it the temperature, amount of sunlight, or something other? And secondly, if it's possible, how would I encourage a domestic Winter White to be one color or the other?
You could try to keep it outside, otherwise it might get difficult.
Just like a lot of other animals, the change in colour occurs depending on the amount of light the animals are exposed to. Since hamsters living in captivity are usually not exposed to the sun outside and not exposed to the changing in the length of days, their colours might not change.
Or as Wikipedia will put it:
In captivity, this does not usually happen as animals maintained as pets are generally housed indoors and exposed to artificial light that prevents the recognition of short winter daylengths.
If you are willing to go that far, you could try to simulate the lengthening and shortening of days.