Animals raised in homes, without needing to provide for themselves, with a warm place to sleep and a nice bowl of pet food every day, are NOT necessarily going to survive if left on the street in the middle of the winter without a source of food.
So they’ll die. That’s what happens to animals. They die. Sometimes you eat and sometimes you get eaten.
I’m not aware that the concept of not causing tzaar to animals includes going out and rescuing them from tzaar.