'Too cold to snow' is also a phrase used in England. I suppose it could have some merit, the amount of moisture air can 'carry' is related to temperature; the warmer the air, the more water it can carry, implying really cold air can't carry water, so it can't snow or rain. The niggling point I have is that if you have warm, water laden air, travelling over your cold region, the air cools, can't hold its water , and it'll rain. If your air is cold enough, this water might well fall as snow.

There is however, I believe a valley in the antarctic where it really is too cold to snow. This valley is so far from the ocean, all the moisture from the air has already precipitated out by the time it gets there. It's so dry there you can see mummified seals that are thousands of years old, perfectly preserved.