I believe it depends on the type of horse you own. I have two horses (well ones my moms but we basically 'share' them), my horse Starlite is the alpha and is always telling other horses what to do. Dream, my mom's horse, HATES to be alone. I couldn't imagine ever keeping her alone!
One time we had to move Starlite to a barn with no other horses and she LOVED it! The neighbors had horses but she had to go far up in the pasture to see them, when she felt like it she'd go see them but it was rare when she did.
Starlite seems to stress with too many horses. As of now she's happy being pastured with Dream and bossing her around, Dream is happy taking her bossing. LOL. But really Starlite would probably be happiest all alone.
It allllll depends on the individual horse.