We fed alfalfa to the Arabs in high school, when I was showing, and it was common for show horses. I think it's become a lot less common, the feed stores stock much more orchard grass than alfalfa, and alfalfa is mostly fed to cattle. It's cheaper than good orchard grass.
I actually think many have come to realize it is more protein than most family horses need, and most vets don't recommend it except perhaps for horses in really hard work.
Around here alfalfa is more expensive then the grass hay.
The particular group of vets that use it recommend that that is ALL a horse needs. The stuff they bring in and use tho you can't even find growing in the field here, let alone hayed. I've never seen stuff so dark green.
Becky