I caught a coyote in late February one year. Only visible hair was a tuft on the tip of its tail. I have no idea how that thing survived the Winter. It had to have been living in someplace that had some warmth.

When my kids were little (20yrs ago or so ) I spotted a coyote in my front pasture that was probably 90% hairless.

It was sub freezing and spitting snow.

I went to get a gun to put it out of it's misery and by the time I got a gun unlocked and loaded it was nowhere to be found.
I felt terrible for that poor thing as it surely suffered a terrible death.

Dad was deer hunting once near some stored rolls of hay, looked away from hay a minute and when he looked back there was a coyote with bad mange standing near the bales. Dad figured he had been burrowed in between the bales in the empty space underneath so it could stay warm

I don't want to see any animal suffer a terrible death
And when numbers reach a certain level there is a dieoff resulting in terrible deaths for a lot (mange, distemper, etc)