been towing all over the western USA since the '80's, much of the time with my '65 Chevy van as the TV, now with a Suburban. I think the curvy roads are the most fun, sure beats long interstate stretches. Lately we like taking the blue roads (two lanes), we see a lot more country, less crowded and more fun to drive. We go around 60 MPh.
The winds are the worst on flat land, where they can come roaring along without hitting obstacles like mountains, plus there are no trees to indicate they are blowing in the desert so you can get hit with a rogue wind that can push you into the other lane (bad if you're on a two lane road). Had to pull off a couple of times with the flat front van, cause I could hardly make any headway against a strong headwind. As others have said, pay attention to weather reports and stay off the road if it looks bad.
I have a Mountain Pass book that lists all steep mountain passes in all western states, it gives me exact location where the uphill starts, how steep it is (% slope) mile by mile, where the emergency ramps are for semi's, how curvy the roads are and of course elevations. It mentions whether or not trucks can make the curves and recommends trucks take another route, and tells if there are passing lanes or not, or is 4 or 2 lane, and even how narrow the roads are. I have altered our planned routes based on this book.
In Colorado and other states with mountain passes, they usually post signs at the bottom of the pass what the slope is and whether or not you should use it if you're towing. We tried one in Utah that said don't use it to tow, and ended up almost losing our brakes on the downhill side. Going down is worse than climbing. Some slopes can be 10% or more, I avoid those now.