The best thing you can do is get one of the many complete horse owner vet books. Amazon is one place you get them.
The biggest and most common thing you'll probably hear about is colic. Colic can happen because of stress, getting into grain, weather changes or no specific reason. It can be deadly. So that's one illness you'll want to become familiar with.
Unless it weighs a ton... it's just a horse. Draft horse motto.