Ever since I had pets, we have included them in our Christmas celebrations. They sometimes had their own stockings and sometimes they shared them.
Last year was the first Christmas with our "son of a feral cat" and domestic mix. It was a little spooky so decorating was limited. Still, I had to spoil him with a few things. He receives gifts for Christmas in July too.
I made a mistake last year when I bought him a drinking fountain for his Birthday just after Christmas. He almost electricuted himself.
On Christmas morning, it was quite entertaining to watch him try to squeeze into the paper gift bag his presents were in. He doesn't fit anymore, but he still tries to squeeze into shoe boxes, tissue boxes and the paper gift bag looked like a kilt. What a hoot! He tore it open to get free. We would have helped, but he was actually having fun.
There's a lady down the street from us who is an old friend of the families. She has a three-legged cat, a blind cat and a seeing-eye brother for the blind cat. (Actually the seeing-eye brother ran away last spring after a showdown with the three legged cat.) Anyway, I always leave her something in her mailbox for "the boys" as she refers to them.
We also exchange gifts with the lady next door and her cat.
Once when my dog had three pups left from her litter we placed them into our Christmas stockings and a photographer from the local paper came by and snapped their photo and we placed an add in the paper. The old dial phone rang for a week with replies.