Welcome to ATP!
Alfalfa is perennial, and I think there is some variety of alfalfa willing to grow in almost every climate.
I would look through a list of cover crops and pick ones that were perennial through whatever kind of winters you have, and suited to your climate and soil.
For example, some tolerate heavy clay and some tolerate hot summers. Some tolerate dryland. If you say more about your climate and soil or region, more people may be able to make suggestions.
I always think "ask the feed store clerk" for advice local to my area.
If you can buy small amounts of several seeds, divide your field into plots and try several different things the first year.
If your goats produce more milk than you drink, maybe you could swap milk for hay or grazing privileges (or seeds). Especially if your goats will eat things that someone else's chickens or cattle don't like.
Around here, one guy made a business of renting his goats out for weed clearing. If you trust someone with an overgrown yard NOT to have sprayed with herbicides and insecticides, he might let you graze your goats for free. Or ask a real estate agent trying to sell a yard that hasn't been maintained.
'Tyfon' Holland Greens are annual, not perennial, but they are cold-hardy down to 10 F and produce a lot of foliage. If you get yours to go to seed, you could re-plant from saved seeds. I mention it mainly because I like Brassicas, and this is a "salad, fodder or compost" plant.
BTW - what with the difficulty of weeding around perennials, I'm start8ng to think that annual flowers are LESS work than perennial flowers! But that's in poorly-managed small raised beds, not a whole field dedicated to one crop.
