The answer to your question, "Will the pools be warm enough to swim in December?" is multi-layered. Both the Big Dipper and the Beach House pools are heated to 84F, as are most every Disney pool. However, the Big Dipper pool is lifeguarded, thus the "feels like" temperature must be 50F or above for you to swim in it. Most December days in HHI the temperature rises above 50F, yet if the outside temp is, say, 55F and there's a stiff wind of 12-15 mph (as it was last week a couple of days), then you will not be able to get into the pool. You may sit on the pool deck, though. Conversely, the Beach House pool is not technically lifeguarded, thus the "feels like" restriction isn't in place--swim at your own desire.
Certainly, that brings up the notion of what is comfortable to you and your kids. Most kids are good to go at 40F

but I would not be. While HHI has more above 50F days than below 40F ones, they still do have very chilly days, especially if it rains. Still, the Beach House will be open every day, so if you're daring enough and the Big Dipper pool is closed, the BH pool should be available.
As to special activities, there will be some minor things such as activities geared to the holidays (wreath-making, e.g.) and perhaps a few holiday-appropriate items, but the full schedule and menus aren't currently available and won't be for another few days. Moreover, some of the Shelter Cove Marina boats are decorated with lights and figurines. A 10-12 minute walk to the Shelter Cove Towne Center will lead you to a 20' Christmas tree and walking tour light display. There is a tour of wreaths and some lights at the Village of Wexford which is less than a 5-minute drive from the resort. Harbor Towne also has a display, but it will cost you $9 per car, per day to get you into Sea Pines area, and why do that when you already have displays and great restaurants outside Sea Pines? About four miles down the main drag (Wm Hilton Pkwy) in the direction of the bridges leading to Bluffton, Firehouse #3 does an excellent drive through lights exhibit, and, finally, you can always Google light displays in Bluffton for more if you wish.
Pretty much every restaurant and shop is wide open during the holidays, though many will be closed on the actual day itself, naturally (and perhaps the day before). In short, there should be plenty for your family to do outside the resort. At the resort, keep your eyes out for s'mores at the campfire (weather permitting), play all the yard games scattered throughout the grounds, and you can always do a movie night in your room--the Mercantile lends movies for free or bring your own, of course.
Hope this helps!