Most horses are okay with little to no protection. I prefer my horse to wear float boots, a tail wrap and a rug, just to be safe and make sure she doesn't get any cuts or scrapes, and also to make sure her tail doesn't get tangled or rubbed. If it's your horse's first time in a trailer, they might be a little nervous, but what you've prepared shoul be fine. You might want to consider a rug if it is cold, but also to protect from little cuts. Some horses also wear fly masks in trailers, to protect their eyes from dust, you might want to consider that too, although it's definitely not a must.
Whoever said money can't buy happiness didn't know where to buy a horse.