Yes, you can graze horses in trees, with special management. It's called silvopasture:
Silvopasture » USDA National Agroforestry Center (NAC)
I would NOT clear all of it out. The land is developed under trees and removing all of them would make it susceptible to erosion, weed infestation and loss of grasses. You can selectively clear it out, though to make it a little easier to move about, and to help sun get to the lowest plant level so that the grass can grow stronger.
Silvopasture is actually quite genius!