Establishing pasture is not a short term activity. Ideally you would do 6 months to a year of just weed control before seeding and then once seeded a minimum of one season (at least three months) before just turning the horses out for a couple of days after mowed to a height they will graze - where they graze then you mow if anything else comes up. Then allow another several weeks before repeating. So mow to horse favored height, graze very short term mow what they don't eat along with the rest to recommended. lather rinse repeat. So much easier just to keep them off for a year and you mow and maintain so roots can establish and residual weeds can be controlled.
Cool season grasses, you can allow less time as you are not using as a permanent pasture and you know you will be reseeding. I don't remember if you are north where you have summer grass (spring, summer, fall) and then snow or you are further south where you have have permanent pasture and overseed for winter grazing.
Some horse people change their horse, they change their tack and discipline, they change their instructor; they never change themselves.