I put on an event every year for the past five years at Silver Dollar City in Branson, MO (you may remember that Dollywood used to be known as SDC), it is owned by the same family (The Herscends NOT Dolly Parton), and the parks are very similar.
It is the 1st saturday of December. It is usually cold, the warmest its ever been is in the 50's, and two years ago they were using plows to haul away snow IN the park while we were there. Yes it was cold enough for snow to still be on the ground, in abundance in the middle of the day. My husband and I and our usually 25-50 attendees have a blast EVERY year.
I dont know if Dollywood decorates for Christmas like SDC, I am assuming it does, but the decorations are worth in themselves. Just be aware that most of the thrill rides (coasters) will probably be closed. Except for Blazing Fury that should still be running, with no water. (we have a similar ride know as Fire in the Hole).
I love SDC, especially at christmas-time, and have come to think of it as the SECOND happiest place on earth.
Jennifer