I just returned from a vacation in Alaska. In Fairbanks the temperature can go down to -62°F (-52°C). At those temperatures unprotected human skin can develop frostbite in minutes.
Animals have fur, of course, but the pads of their feet are not covered in fur. I am thinking also of sled dogs, not just wild animals.
Just a guess here, but maybe they have adapted to it over the eons by having more/larger blood vessels in their extremities to keep more core-temperature blood in those areas.
They do get frostbite. In which case they A) heal B) cope C) die.
Specifically for the pads, they may not be as affected by reduced bloodflow as other parts of the body. It would make sense as pads act as a buffer with the ground.
It does happen.
Here in Minnesota, we often have rescued cats with frostbite on their ears or tails. Sometimes severe enough that amputation is required.
During my vacation I went to a presentation on dogsledding by Tekla Monson, the daughter of Sue Butcher, a four-time Iditarod winner. They showed the booties that the dogs wear and were emphatic that they were not for warmth, only to prevent snow and ice from packing into the paws between the toes. I asked my OP question to her and she said, “I’m not a biologist–I don’t know.”
Thanks for that. Very good explanation. It discusses typical domestic dogs, and sled dogs are bred for it so are probably closer to wolves in how they deal with cold.