Gatlinburg's "official" (town sponsored) lodging site is
http://www.gatlinburg.com/lodging/
They will list most of the available lodging in Gatlinburg proper. You will find better rates if you get off of the "parkway" (i.e., Highway 441, which runs through downtown Gatlinburg). Hotels along the River Road are nice. There are some hotels on Highway 321 (East Parkway) that should give you some good deals. Some of these hotels, however, have outside pools.
Perhaps the best indoor hotel pool in Gatlinburg is at the Park Vista. It is nothing elaborate, however. You might also look into staying at the Wingate Resort right outside of Gatlinburg along the Parkway. They have a nice indoor pool area. Neither of these options will be the cheapest, however.
If you don't mind staying further outside of Gatlinburg, try Pigeon Forge hotels. They usually run a little cheaper. Some places, however, are real pits so be careful.
Don't be afraid to call the hotel directly and ask for a better rate. As a whole, Gatlinburg/Pigeon Forge isn't doing too badly in this economy and December is a busy time of year for the hotels. There are still a lot of hotel rooms in the area.