I regularly take my short-haired dog camping in cold weather. Here is a list of his gear for sleeping.

His bed

His jacket

He wears the jacket to bed when it is cold. The bed sits on a cheap-o blue foam pad, cut in half, and double-stacked. Then, I drape a cheap-o fleece blanket on top of him. He sometimes gets up to stretch and turn around, but the colder the temps, the less he does it. Usually all you can see of him is the tip of his nose poking out from under the blanket. When he does get up, it wakes me and I am able to tuck him in again.