All the fans have screens, but dust and insect parts can get through them.
I asked a guy at Fantastic Fans whether a fan cover had ever blown off. He said they will send you a new one if it did, though it was very rare. I don't want to tape over the hole if one did blow off, but my wife decided to keep them closed anyway. Since I've had problems with the bathroom fan leaking, anything that stresses it—like driving with it open—is not something I want to test.
I've thought of getting the covers, but didn't want to spend the money and put more screws in the top of the trailer.
In an hour, a trailer can get very hot, though less so where you live. You could run the A/C at 60˚ before you leave and cool the interior, but I suspect it would heat up anyway. With a high ambient temp on a sunny day, these trailers are not well insulated and bringing more hot air in isn't going to make much difference. Think about a car on an 85˚ day with just the vents open—it gets hot fast. Faster with the vents closed, of course.
So it doesn't make a lot of difference I think. The thing I worry about when we're traveling is medications in the trailer—they are supposed to be at room temperature, but the trailer can be more than 100˚. I have to remember to keep them in the fridge.
The best thing would be flow through ventilation like cars and trucks. A vent above the front and back windows with a filter at the front one. No fan necessary. But I doubt that's what you need right now.