My grandson's cat wants outside occasionally. He'll try to scoot out the door if you don't watch out for him. We will let him 'slip' by sometime when the ground's covered with snow. He'll bound out, quickly stop, look back at the door, and look at us like 'What are you trying to do to me?!!) Sometime we'll let his stand there for a few seconds before opening the door to let him back in.
I've got a little chi/terrier mix. She'll be 14 years old in February. Her back stiffens up at times when she's been sleeping in the same position for a while. When I let her out in the snow, she'll step off the little porch, urinate, and quickly run back in when I open the door. Sometime she has to spend a little more time ou. I've thought a few times in the last couple of years, that I'd have to go out and bring her in. She will get part of the way back to the door and start staggering like her right rear leg is giving way. Then the leg seems to bother her for several minutes until she gets warm again. She was given a little 3 step 'Up and Under' for Christmas. It's to help her get up onto the bed without having to jump. Although I've got her to use it several times, she still jumps up onto the bed. I'll have to wait and see if she'll use it after she' been out in the cold for several minutes.
The other dog, the grandson's, likes to run through the snow; but only for a little while. Then she wants her paws cleaned and dried. 'Course, like most dogs, anything for a little attention!