Luckily horses do not _need_ alfalfa. Farmers love growing alfalfa because if you give it sun and water in the right setting you can get damn near 14 cuts off a field of it in one year. This by comparison puts a grass hay field or even a nice neutral horse feed, Timothy grass, to shame. Alfalfa is a nutrient dense power bar that is given to horses kept in boxes. I would argue a happy horse would have a range of grassland to graze on, vs compressed cubes or squares of dense, sugary alfalfa that is replacing a normal ration.

tldr: alfalfa is an unnatural food for unnaturally kept horses

source: have horses on range land.