Cataloochee Ski Area is open if your family likes to ski. A friend of mine just got back from there this week. He'd taken his 5 year old skiing. He started last year and is getting pretty good!
The rock shop in Maggie has always interested my kids (10 & 7).
Cherokee is always fun to visit. You can go on from Cherokee into the Great Smoky National Park. Newfound Gap usually has snow and ice this time of year.
If you gone that far, you might even try Gatlinburg / Pigeon Forge, TN. Lots of fun there.
As far as restaurants, J. Arthurs is open year round. Great steaks.
Joey's Pancake House is only open for breakfast. You may have to wait, but it's worth it.
Granny's Chicken Palace going into Lake Junaluska has very good chicken.
If you go into Waynesville, historic Main St. is beautiful, with several coffee shops, art galleries, restaurants, etc.
Maggie's Galley in Waynesville has super seafood.
Sorry this is so broad. Let me know if you have something specific in mind and I'll try to help.
Have a great trip!