there are no blankets sold specify for trailering. A cotton or fleece one would be fine. If my horse is wearing a blanket outside, he usually wears it if we trailer any wheres as well. Though, keep in mind, we usually don't travel far, 15-20 mins tops, and my horse isn't one to get nervous on the trailer and sweat.
If i was to travel any farther, it would depend on the weather, if it was winter time, i would probably just put on a fleece/cotton/rain sheet instead of his winter one, and in the summer he wouldn't wear anything anyways.