your only thinking one dimensional. You can say the same thing about color. Why is it in solid objects white is all the colors combined. But when dealing with light the color white is actually the absence of color. Hence why in hexadecimal form white is #000000 instead of #FFFFFF (Black).
Thermal imaging is just that, an image produced with in the sight based of off FLIR. So it would be very easy to write a program that says display something hot as black, white, red. Whatever.
So to answer your question. Real snow is white because it contains all colors. Fake snow on a television (like in the game) is white because it actually contains no color. And snow on a thermal sight is whatever color that thermal sight is programed to show when something is cold. Got it.