I have been on both sides of the fence on this one; with some horses, it is better to have some sort of companion. With others, they get along fine without one. I have always had a goat or two, as there have been times when my horse was boarded alone. He was perfectly fine having the goats as his companions. They never chewed on his mane or tail either. I think that goats do that more because they are lacking something.
My current horse could care less about other horses, really; you can put him in with anyone, and he'll just amble off in the other direction...he would probably do fine as a single horse.
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."