[Dodge]

I've been towing my T's an A's on an open trailer for 50 yrs. no issues.
The one T with a glass visor I tow backwards to avoid damage.
The shrink wrap is a great idea.
One time we did bring a car back across county when we knew we were going to be hitting bad weather. We put in in the back of a U-haul truck using a transporters rear lift gate at each end of the country. There was a sign on the wall of the rental place that said "No complete cars in the truck" so we left the radiator cap off......