I do not leave mine up when trailering. If I was only going a short distance at a low speed I would probably leave them up however for highway speeds I would not. My $.02
I have also been told not to trailer mine with them on. They can rip and the one time I did do it, the windsheild was covered with bugs. So I learned that time, to just take the extra few minutes when you get OTW and do it there. In cold weather it sucks because they dont stretch well, so I learned to carry them in my truck and let them warm up in there.
Here is my 2 cents if you are going 35mph or under you can probably get away with it, especially if it is a short trip like Salty said. I go that fast with it up on the water all the time. Beyond that forget it. If you don't take it down before you leave you will be taking it down on the side of the road
I don't leave the side curtains on but I keep the middle section on and up all the time. I have been doing this for 7 years with the same setup and have never had a problem. That even includes some trips on the interstate at 65 to 70 mph.
My guess would be it all depends on what your setup is like in terms of attachments and aerodynamics. If it isn't connected very well or wind can't get over and around it as high speeds then you are going to have issues.
This is the boat with out the plastic and canvas on. they are snaps and zippers spaced about 8" apart. They go from the hardtop to the winshield and wrap around the sides to the back and down to the deck
I think I will travel with them off until
I at least try it on the lake all set up.