December is a pretty good time to go, if you ask me. Usually the park isn't too crowded (except on the holidays themselves, which can be pretty packed). The weather is chilly, so lots of folks pass on sitting in the 'splash area'... which means better seats if you're willing to risk a little water.
As for the weather... Florida is the sort of place where the weather can change in an instant. One day may be mild and sunny, but the next could be rainy and miserable. (Or one /hour/ may be mild, and the next /hour/ could be miserable!)
But in general, you can expect mild-winter temperatures in December for the most part... average highs in the low 70s, average lows in the low 50s. This can vary, though.. and we're known for getting sudden cold snaps which can drop us into the high 30s at times. Rain in the winter isn't the daily drenching we typically get in the summer, but instead it's usually a thick line of heavy storms ahead of an advancing cold front.
It'll probably be too cold for Aquatica, and possibly for less hardy souls at DC (I've done DC in December, though... it wasn't THAT bad)... but just fine for SW!
As for New Years itself, I rang in 2000 at Sea World.. the only time I've ever done a NYE there.. but it was a blast! Not quite as fancy, I imagine, as Disney might offer... and a little too saturated in that country music that Sea World falls back on so often... but it had special meaning for me, as it WAS the new millennium and Sea World IS an important factor in my life.
All in all, I say go for it!
=)
