Watching the "Mountain Trip" scene (again!) in "The Long, Long Trailer," I would say NO!
Then again, that was the 1950's, your trailer is WAY smaller than Lucy's & Desi's and the roads are WAY better now.
Just adhere to the tried-and-true Mountain Driving Rule #1: Go down
the hill at the same speed you went up
the hill... And you'll be OK.
John E. Baker, III and Sally Baker... The Traveling Siblings! — Watch your tail swing... Keep the greasy side down and keep it 'tweeeeeeeeen the ditches, Y'all!