Congrats on the trailer!! Just bought one myself, and needed to put new tires on all the way around because where I live, dry rot is much more likely to kill your tires than pretty much anything else. You've already won the first battle, because you know to buy TRAILER tires, and not just AUTO tires
As was mentioned, trailer tires have special load ratings to help support the weight of the trailer and horse(s). From researching, I found that Maxxis M8008 and Goodyear Marathons are consistantly rated well. I bought Maxxis and paid about what Darrin did for his. Just remember to keep the best (or buy an extra) as a spare. Also, pay attention to the PSI ratings. Trailer tires run at a much higher PSI than regular car tires, hence the need for higher load ratings
Good luck and welcome to the club!