One of the two water parks is closed that time of year. Some days it is so cold that both water parks are closed.
Weather can be all over the place in winter, so the crowds can also be quite variable. If you happen to get a very nice day, the water parks won't be empty. They shouldn't be too bad Christmas Day though. We didn't go Xmas day, but we went that same week on a VERY nice day. It was busy, but not too bad.
Specifically on Christmas day, I expect many folks don't want to risk missing their ADR's. Since there's a risk MK will fill to capacity; I'd bet many folks arrive at MK fairly early and don't leave. Probably Epcot as well. (though the capacity risk is lower.)
Just be prepared that your plan might not pan out if the weather doesn't cooperate.
[this fall/winter BB is closed 10/23-12/24. TL closed 12/25- to 3/11. You are correct, Xmas day BB will be open.]