You don't mention what Tow Vehicle you are using, but it should be no problem if you have a capable TV. Any 1/2 ton big three brand pickup with the tow package for example.
We have towed RV ranging from pop ups, small and medium sized Trailers and now a fifth wheel all over the west and mostly on non-interstate roads. We actually had one big problem, we blew the rear differential on a Suburban we were using at the time, coming down Pike Peak. That was mostly my fault for not knowing how to downshift correctly. Or when to pull off and let the vehicle cool down when it needed to.
That was 20 years ago and we've learned a lot in the intervening years.
Just take it easy in the mountains.