In below freezing temperatures, it sounds like a very GOOD idea...

Sure, but there are other ways to keep your water bottle from freezing, such as keeping it in an insulating bottle parke, upside down, keeping a hydration pack in your pack along with the tube in an insulating tube (this is what I use).

The idea of keeping a water bottle next to my body doesn't sound very appealing to me... especially while snowshoeing with a backpack, waist strap, etc. But for a small walk without much gear it might work.