It may be a better option to simply overseed the pasture by the method most suitable for the situation. With a small field, it may be best to simply spread seed on the soil surface when damp, if possible after harrowing first. Rolling, or grazing with sheep, will help establishment. Some useful facts Avoid over or under grazing. Avoid over or under grazing.
Horses are notorious spot grazers.
They will seriously damage desired species in some areas unless they are moved into new pastures frequently. Therefore, some form of rotational grazing is desirable. If you expect horses to get most of their nourishment from grazing for most of the year, with limited supplementary feed, you will need at least 1 acre per horse and good pasture management. If you want to make your own hay, you will need at least one more acre per horse. If reseeding, you want a pasture mix with a good balance of early and mid season perennial rye grasses.