Are there any regular holiday events?

There are only a few special events in Diablo 3 that I'm aware off.

Last year, at the end of the year, they did a 20 year anniversary celebration of Diablo Its possible they may bring it back this year.

Other than that, they occasionally do an event called Double Trouble where all treasure goblins spawn in pairs. This is not a regularly scheduled event but it does come back around every once in a while. They just had one right before season 12 started.

The vicious gray turkey is not part of any thanksgiving festivities, he's been around for a while now. You need to kill him as part of a cheevo for killing all the unique named monsters.