Not sure it counts as a tradition or not, but I always try to take Alfie with me to my parents house on Christmas. I then sleep over at theirs and he gets to help eat the Christmas dinner and boxing day dinners. (He likes my mum's cooked veggies but doesn't touch any that I cook for him... favourtism!! 🙄)
I say 'try' to take him with me because I have to convince him to get in the travel cage first. He's getting better at it but in previous years I have had to leave him at home because he took himself back into his cage rather than going in the travel cage then refused to come out! This year he stepped into it on the first time of asking, which is a first! When it happened I was so shocked I said it was a Christmas miracle! Normally he likes to give me the run around before getting in it.
I can't wrap presents for him because he loathes wrapping paper. He growls at it. He wasn't too bad with it this year when I was wrapping presents because I used brown paper rather than the usual stuff, so it looks, moves and sounds different I guess. However, I didn't buy him any toys because he has quite a few new toys that he hasn't touched yet. I'm also planning on getting some food, treats and new perches in January.
The cats got their Christmas present early at the start of December- they got a new cat tree!