I worked on a legal case once where a grain mill delivered a load of feed to a cattle ranch containing Rumensin and went back for a new load of grain to deliver to a guy who owned a bunch of horses. I can't go into any detail (for obvious reasons) but that guy lost something like 35 head of horses of varying ages. Some within a day or two and the older ones had to be put down because the heart damage made it unsafe for them to do their jobs. The only grain they ate was horse quality that had touched a truck used to haul a Rumensin feed.
OP, I have 2 goats and my horses don't like them. They are mean to the poor goats so I have to tie them out separately. I use them to get rid of weeds and strip the leaves off of tree branches. I like having them around, but won't get any more after these guys die. They are both wethers and descented. Only one is dehorned, but I wish they both were. I personally have never had my goats jump on anything or try to wreck stuff. They are both collar & lead rope trained though. If they get loose the first things they go for are any landscaping my mother has done that cost her a bunch of money (They looooove expensive bushes & flowers - so much tastier than regular grass, lol) I also have never had a problem with them chewing horse manes & tails, but some people have.
Taking care of them is pretty easy. I just feed them hay I have swept up off of the floor or crumbs left over from my horses. If that isn't enough, I toss them a flake of hay. I quit feeding them special goat chow because they just sorted through it & ate what tasted best. I don't feed them any grain, but they love snacks. Any fruits, veggies, or lettuce that is going bad, we feed the goats. They go nuts for the last "half crushed won't make a decent bowl" part of any cereal we have (especially froot loops) You should also know that goats will need their feet trimmed. I do mine only about 4x per year and they also need to be wormed. You really can't use equine paste wormers for them. I think quest and safeguard might be the only ones?? I give them Sub-cutaneous ivermectin shots.
If you get a mini - be careful because they require all the same things a horse does, but can get sick more easily from not having their diets watched closely. You really couldn't get one if you are planning to turn them out on very lush grass. I have heard that mini donkeys or even a small regular donkey rarely have problems with founder, so that may be a better choice than a mini horse.