For those who want to see a bit of natural beauty but don't want to freeze outside, consider taking your dog on a drive through Cades Cove. The 11-mile driving loop features tons of wildlife and beautiful landscapes you can't see the same any other time of year.
If you want another fantastic place to do some indoor winter shopping, check out the Great Smokies Flea Market in Gatlinburg. The largest of its kind in the state, it offers a massive variety of goods, is open year round and of course, is also dog-friendly.
If you don't live in the area or just want somewhere to get away to, consider renting a dog-friendly cabin or Airbnb in a city nearby some of these attractions or up in the mountains where you and your pooch can curl up by a fire and do some reading after frolicking in the winter wind.