WE have driven the length of the BRP several time in our various coaches. The present coach and the previous one were 36 footers. The drive is slow, speed limit 35 to 45 and it can be hard to maintain that safely in a coach. It is twisty and can be steep, we love it! None of the "attractions" or parks along the BRP will be open nor will any of the lodges.
The real issue I see is getting off the parkway if it starts to snow. Many of the "roads" are forest service routes suitable for my Jeep. Many of the paved roads that come down off the parkway are very steep and twisty, especially if you are in the high mountain areas. Even getting off at Rockfish Gap, the northern end of BRP and the entry to Skyline drive the descent into the valleys is very steep on the main roads. Just something to be aware of, it can be done but you need to put away the Florida "flatlander" mentality. Some people think mountains in the east are tame, they are not! Especially when covered with snow and ice.