The thread on keeping your face warm while sleeping outside in winter inspired this question. How cold does it need to be for you to get a frost-bitten nose despite keeping the rest of your body warm?
Would it be different than the conditions for getting frost bite after losing a glove? Would core temperature need to start dropping before blood flow to the extremities started decreasing?
the skin has to get below freezing to get frostbit. your body can be very warm and you still get frostbit. the outside temperature doesn’t have to be that cold. if you caused heat to rapidly be extracted from a small location then you could get frostbit; e.g. if you had a below freezing temperature and lots of wind and spill gasoline on your fingers, licking a flag pole.
In cold enough temps (-30F or so) any exposed skin is at danger of quick frostbite, or at least frost nip. The tip of your nose, ears, the skin atop your cheekbones, fingers, and toes are the most likely areas due to blood flow patterns and/or they’re commonly exposed. In temps above that you can accelerate the chance of frostbite by touching metal, getting wet and exposing the skin to wind, or poor circulation due to many factors (dehydration, lack of food, drugs/alcohol, illness).
I’ve seen and had frost nip (a lesser form of frost bite without skin being frozen full thickness) at about +10 F.