Most years there is no problem, but the typical weather for the area is highly variable. Just watch the conditions the week of your trip. It is extremely rare for an extended forecast to be useful to make that drive.
This year has been much warmer and much dryer than normal. If the current pattern does not change, you are just as likely to get road closures due to fire and smoke as weather. The US Forest Service has already moved a 'Sky Crane' fire fighting helicopter into the Macon County NC airport in anticipation of a bad fire season. 2016 was the year that Gatlinburg came very close to being being totally lost, and this years fire conditions for the area are just as bad or worse in the area.