I'm a juvenile diabetic, so I definitely have to watch out for circulatory problems like frostbite. If I lose part of my foot, I doubt I'll be any better of a hunter. The coldest weather I've hunted in was 20°F, with a light wind. I bundled up with plenty of layers (and toe warmers), and the only problem I had was that my left middle finger went numb halfway into the hunt. I flipped off the deer that were still hiding in the treeline for a few minutes and it started to warm back up.

I don't think any weather's too cold as long as you're dressed properly and can still move about easily.