This question has come up before and I am not
certain if Susan Garlinghouse was the one that answered it or not. The
advise I recall was that it would be a good idea to supplement some alfalfa in
your horse's regular diet at home if you anticipate them eating it at a
ride.
I don't regularly feed alfalfa but during the
riding season I will get a few bales and every day give my endurance horse/s a
small flake. At the end of the season they go back to having only their
grass hay.