Just went from Gattlinburg to Cherokee on 441 2 weeks ago in a car. You will have no problem other than lots of traffic and your speed will be about 35 MPH. Quite a few tight turns but managable in a MH.
Take a break and pull into the large public parking space at Newfound Gap. Highest point on the route at about 5,050 ft. Beautiful views.
Marc & Jan
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