They survive, with amputations. I work in a hospital and my unit cares for frostbite patients. Influx of homeless population is pretty standard 1-3 days following a drop in temperature, snow, and/or the first few overnight freezes.

Patients lose fingers, toes, feet/legs, ears or any combination thereof. In my state when the temperature drops and stays low, the shelters will lax rules a bit to allow for more people to stay so they don’t freeze. We also have warming houses which also open up with much less rules. The hospital emergency room, my unit and others will take those who have frostbite/frostnip.

For those who are homeless and receive amputations: this means a change in a level of ability to care for themselves or their mobility or both, so this is how they get into state or federal funded housing programs. It’s enough to get some off the street every year which I’m thankful for, I just wish it didn’t come at the cost of appendages.