Birdsfoot trefoil is hardy, tolerates grazing, makes good hay, etc etc. It has only one problem. Horses don't like it. They do eat some of it, but they don't like it. I'm trying to get rid of mine.
White clover is about the only choice left.
Go to your county extension office, get a soil map, and figure out what your soil type is. Get soil tests done, and fertilize as recommended. Seed with a grass-legume mixture appropriate to your climate and soil type. The extension office will have lots of helpful bulletins on pasture and hay, but don't expect the extension officer to know much about horses. Mow your pastures at least twice a year no matter how short they are, and rotate them.