That safety switch is for old folks, so they don't fall asleep and wake up done on one side.
A dog i would worry about tearing it up, but a cat should be ok.
Just be sure it is ground faulted.
A couple old pillow cases, or a sheet, and some stitches should work.
I'd think.
Most important is getting out of the wind and the wet.
I feel for the neighbor dog, she didn't have a house for two winters.
Some people shouldn't have pets.
I've had to intervene a couple of times around here with neighbors maltreatment of their dogs. I have pics on my phone about one of these dogs, that I'll probably use in a future post about it.