I definitely see less homeless people in places that go to -40 in the winter. Now I don't know why, maybe they still exist but are less visible. Perhaps the threat of homelessness is a lot scarier when it is cold outside. Maybe homeless people in those climates move. I don't know, but anecdotally it does seem like there are much fewer homeless people in cold places.
But you have to have some form of shelter to survive -40, which means that nature itself forces something (or you just die).
(Note the homeless veterans, that's just an absolute embarrassment to the country as a whole; something major should be done like just re-activating them and providing housing).