Goats can be fine with horses, or it can be a disaster. It's best to have a plan to completely separate them if personalities don't get along. I had my goats out with my minis for years until my one mini decided that biting and chasing the goats was in order. One of the goats also decided that attempting to spear my mule would be great fun.
I immediately removed the goats from the mini paddocks and barn and they now have their own area. If you would like to get goats for your minis I'd recommend a goat with no horns. I have goats with and without horns.
I would introduce between a good, secure fence and watch the body language of both the goats and the minis. Then daily - even hourly supervision until you can determine if everyone is going to get along. Having a picnic table or some sort of place where the goats can hop up or get under if they feel uncomfortable is a good idea as well. Goats like to play by hopping on things. It would be wise to have a separate feeding area, especially if you are feeding any grain. Goats shouldn't have horse feed and vice versa. Goats also need minerals that are best kept separate.