My birthday is Dec. 4th, so we've sailed in early December pretty often. I find the ships to be pretty full during this time of year. More so than in Sept./Oct. On our last December cruise, there were quite a few kids, but I couldn't speculate as to how full the club and lab were, as none of the kids were ours.
The pools are allegedly heated, but I find them pretty cold. One of the TV channels in the stateroom gives ship updates, among them are the pool temps. They're usually listed as 80-82 degrees, but I question that. I find the pools colder than the ocean at the Caribbean ports, even in December.