I agree with Sam.
For the horse as long as they won't get to hot, it's safe. There is always the risk of the blamket/cooler/sheet getting ripped though
The short answer is yes, if it is a "dress sheet" style with at least a belly strap to keep it secure, not the square full body cooler. However, keep in mind that horses can get quite warm in a trailer. They expend a lot of energy (and keep their body temperature up) just by balancing during the ride.