You picked a very good time to visit, my friend. It *should* be after all the winter break hoopla has quieted down, you're in time to go Rockin' Both Parks, and most of the off-season refurbishment doesn't start until just after your visit. Except do be advised that the Haunted Mansion will be closed to remove the holiday overlay. And it looks like Dumbo will be closed too. Other than that - great time to visit.
Some of it will be taken down. It's a week-long (or longer) process, as you can probably imagine. Can't say if the tree will still be there or not, but I do know that It's a Small World Holiday will still be Jingling and Belling for your enjoyment (until the 22nd)
Jan is my favorite month. One of the least crowded. On a weekday in Jan last year every ride was 5 min or walk on. I rode Matterhorn, Space Mountain, BLAB, Indy, Pirates, Haunted Mansion, Splash and Big Thunder all in about 2 hours!