The park is open year round with only some roads closing if there is bad weather. Don't think they have had any major snow yet this year. We like the Leconte View, stayed there a couple of times. You can visit
www.gatlinburg.com for some info. If you haven't been to the new Ripleys aquarium, it is a nice attraction to do, but can take a couple to several hours depending on your children, etc. My DS could spend all day there so it usually takes us about 4 hours or more to go through. Ripley's Believe it or not is good but I don't like the newer one as well as I liked the old one that burned. If your looking for some cheap fun you can ride the trolley up to the Gatlinburg community center where they have indoor pool (huge), bowling lanes, pool tables, ping pong, basketball courts etc. We went up and bowled some one year, I think it was $1.25 a game. Guiness is okay but not great. Don't do the World of Illusions, DH and DS did that when we were there in the fall and DH said lots of the things were broken or not working - waste of money. Definately go to the Donut Friar in The Village, they have wonderful donuts and cinnamon bread. The Stars and Cars museum is good (DH wants to go every time we are there but to me its sort "been there, done that"). There is a neat indoor gold, Treasure Golf or something to that effect, sort of themed like Indiana Jones, its right on the parkway. If your kids like creepy stuff, the Haunted Mansion on River Road is a neat self guided walk through. You have to find your way through it. Christus Gardens is nice but also another "been there, done that" attraction.
We stayed at Gatlinburg Town Square in the fall, it was okay, (it's a timeshare resort, we rented a studio on some website that I don't remember, reservegatlinburg I think). It's a good walk though if you travel in Gatlinburg mainly by foot. If it was warmer I'd say go see "Unto These Hills" over in Cherokee but I'm not sure if they do it this time of year and it is outdoors so it might be too cold. We are only about 2 hours from there so we take a couple of extended weekend trips up a year.
If you have any other questions I'd be happy to help if I can, either post or PM me.
P.S. - Had to add, if you like Italian food, make sure you go to The Best Italian Cafe in Elks Plaza (Elks Plaza is next to the Cherokee Grill) It's a trip tradition for us.
http://www.bestitalian.com/
Cristy