I'm a bit late responding to this, as Christmas has been and gone for another year. But yes, I absolutely buy my pets Christmas presents. People think I'm a bit crazy, because our pets even have their own Christmas stocking that is embroidered with their name on it. They are as much a part of our family as anyone else so it wouldn't feel right not to get them something as a gift.
As for what I get for them, it depends. Their Christmas stockings always contain some food based treats that they like, a toy of some description, and the Christmas just gone I also got them new pet beds each. They usually sleep on our bed anyway, but the pet beds are good to take if we are traveling, and plus they were just really cute designs so I had to buy them!
We also got our cat an outdoor mesh cat run for the yard, we ordered it on Amazon. Our cat likes to go outdoors but we're too scared to let him simply roam free, in case anything was to happen to him (I've had a cat that sadly was hit by a car several years ago, so I don't like leaving our current cat outside unattended for any reason). The mesh cat run is good because it is spacious, nice and breathable, and has podiums and a hammock too for our cat to jump on or lay in. I think it was a really good gift to get for him, because it allows him to enjoy the great outdoors but gives us the peace of mind that he's not going to run off and get into any trouble! He loves it!