My DH is the same way, fan must be on no matter what the temp. All 3 sleep with us and they move about as they need. In fact I count on them to help
me in the winter to stay warm.

I've put jammies on Gracie Ruth a few times this past winter but for the most part if it's too cold for them, they just burrow under the covers and cuddle up next to me and we all stay comfy toasty warm together.