It really does depend on the horse :)
I had a filly who needed a companion for romping about with. She would try to play and at the time, that was just a wee bit to scary for the fragile human O_o
My older rescue on the other hand, does great alone. He's a very slow, easy going guy who's just fine with human company. The younger geldings just annoy and push him around. A burro, mini, goat, or another old dude would make a good companion, but it isn't needed. He does pick up more on habits like pawing when he is alone though.
My nine year old would do just fine and dandy alone. He is VERY dominate and would probably try and kill a burro or mini. It's either another submissive horse, or no horse.
My three year old is kinda iffy. On the one side, he loves having other horses around and likes to stick close to the dominate member of the herd, but on the other hand he's starting to warm up to people and see they too, as a source of love and protection. He was never abused, just not really worked with since he was a yearling.
It also depends on how much time you are able to spend with your horse. If your only able to spend a few hours a week (other than feeding) with them, then a companion animal should be considered, or toys should be bought. Horses get bored too x)
Wait! I'll fix it....