Do you have to go to college if you what to be a horse Breeder or a trade school?

I doubt many high schools have classes designed for what you want, however, I would highly suggest some Business courses and Statistics. If you are a breeder, business savvy would be an asset for you.

In college there are specific colleges and universities that specialize in classes in Horse Husbandry. There are universities that have riding teams, and if you are good enough you can qualify to be on the Olympic team. I would highly suggest you start searching the internet for these specialty schools so you can make a choice which will meet your needs.