My gelding had two goat companions while he was on lay-up in a medical paddock. He did okay. I think he enjoyed the company, it was better than nothing. Later when we pulled the goats out, he would sleep by the chickens instead. He is not super social, but I think he does long for the structure of a herd. He is definitely more secure when he is turned out with horses.
The positive was that they did provide a pretty enriching environment for the gelding. They play a lot, and would raise holy hell if you pulled him out of the paddock without them. They’d bleat so loudly. He never called back, but he was always watching them during grooming sessions.
The biggest problem I had with the goats is how messy and wasteful they were. They would trample, sleep, and pee on my gelding’s hay. My gelding’s hay was always put in a hay net and even then the goats would leave a mess. For every flake they pulled out of the hay net, they’d eat one or two wisps. On his own the gelding cleans up a flake very well (including any on the ground), but with the goats 50-70% of it would be on the ground and untouched. Fine in the goat paddock, not ideal in the stone-dust medical paddock.
The worst part was grain - my gelding is very proprietary about his food with other herdmates but for whatever reason that did not translate over to goats! He would just sit there giving me the forlorn eye while the goats annihilated his grain. If he tried to nose his way through the bucket they would butt him. We tried hanging the buckets higher, moving the bucket around out of their reach, but the goats were crafty enough to learn if they balanced themselves up on the fence they could still reach a bucket that was well above their head height - we ended up tying the bucket on a post outside of the paddock and just having the horse hang his head over the fence to eat, but even then the goats were pushy as hell with the horse and would try to get in between him in the fence to get the dropped grain. So we ended up pulling them out before he was fed. Simple enough solution, but they’re goats and had other ideas and you dragged them quite literally kicking and screaming out of the paddock.
Since you already have goats I’m sure you’re aware they’re master escape artists. We had to put chicken-wire mesh around the paddock to keep them in. One of them figured out how to jump the fence and the other goat would absolutely go ballistic trying to get out after him. I find them to be a real nuisance, personally, and don’t know if I would ever get my own. They are a fair amount of upkeep and for someone who is goatless it’s probably easier to just find a companion horse at that point.
Not sure if yours are dehorned, but the ones we had were not and that was probably part of the problem. For a horse on medical lay up, my horse did end up with a lot of inexplicable scrapes and cuts on his legs that I am sure were from their horns. Once the goats were removed he stopped getting them.
The fun all ended when one of the goats nearly killed itself by getting its head caught in the hay net - it was lucky we were around or it would have strangled itself to death. That ended that.
Part of my negative experience with them might have been because they are not very tame, but they weren’t my goats. Yours might be better.
In the end I think they are fine if you have the set up, but my personal experience is that the horse is happier with another horse.