Agree with Rosemary.
My horses have made an excellent job of ressurecting an old pasture that the owner was all for ploughing up and reseeding. Apart from a new problem with moss, which may be related to the mild, wet winter it is good grazing now. Horses don't, as a rule, eat buttercups though, so they can be a problem, but adding sheep and geese helps clear them up and any sour patches horses leave.
I'd say top, harrow and graze hard, poo pick often and reseed any bald patches as necessary. Get a ph/mineral test done by an agricultural consultant and add fert or lime as indicated. And get rid of as much sycamore as possible or at the very least don't graze horses near them in autumn to avoid the risk of grass sickness!