Or are they indifferent or even utterly contemptuous towards it? Our cat many years ago quite liked it, I think. It certainly didn't stop him from going outside to spend a penny and sinking up to his belly. He'd jump and scamper about for a while then come back inside. Our spaniels didn't seem to mind and would still go for walks and accompany us sledging. Having quite long feathering meant that lumps of snow would stick to them which they were less keen on. Like the cat, they'd still go out for toilet duties.
There's some good videos on YouTube of dogs sledging with admirable skill. One or two don't even bother to use a sledge!