Hey Rachel ! In measured amounts it's really nutritious and horses really apreciate it but it's super rich and can cause problems. I agree with Katelyn and Sara and i would recommend to begin very slowly and not let them too much time in the field if they also get hay and grain.
The way we get my horses used to the pasture in the spring is we let them out there for about half an hour and then bring them off. The next day we'll do maybe an hour, then an hour and a half, etc. until they can be on it all the time. However, our pasture is just grass and since yours is alfalfa, I recommend fifteen minute increments instead of half an hour.
I know it seems like it'll take a long time, but it's better to be safe than have them colic.
Hope this helped!