We were able to make reservations for just after Christmas and across NYE this last year without any problems at about 6 months, but we wanted a 2BR unit, which HH has more of than any other.
When we arrived though, we were told that the resort was at 100% occupancy - but apparently most of the reservations were made by people only a few months prior.
The resort didn't feel crowded at all. They had a number of activities for younger kids (a southern snowball fight, fish painting, etc.) - not a lot for teens (that I recall anyway), though they did have a NYE party specifically for teens (with pizza and soda). THey also had the usual excursions running, such as the dolphin watch, kayaking, etc. The pool was open, and frequently on a sunny afternoon day, they would even periodically run the water slide.