We went to the park last year for 5 days during this time. We were there for 3 days before Christmas, the day of, and the day after. The three days leading up to Christmas was DEAD. We always stay onsite simply because we love the rooms and the fact that we are within walking (or a boat ride) distance from our room and we don't have to take a shuttle bus or drive back to the hotel.
Anways, Christmas day was the emptiest I had ever seen a theme park in my life. I mean, it was like a ghost town in some areas. A lot of the stores and restaurants were closing super early simply because nobody was there.
However, the next day was a total change! The parks went from being a nice, slow paced, relaxing, calm experince to a total zoo! We were so glad that was our last day at the parks and that we had so many nice days before it. If you are planning on going, try to go before Christmas, not after. After is by far the craziest time of the year! I got this crazy idea of thinking about going for new years this year and I went and checked on room rates and every single onsite hotel is booked full.