Silvopasture is the practice of combining forestry and the grazing of animals into a mutually beneficial system. People do this by 1) planting trees into grassland or 2) seeding grasses into forested areas. Effectively managed silvopasture operations can enhance soil protection and increase long-term income from the simultaneous production of trees and grazing animals.
If you are going to add trees into the pasture, there are some things to consider - grass selection, tree selection, tree protection. If you are going to add grass to forest, there are other things to consider - thinning the forest, soil erosion, grass selection, tree selection.
A note on grasses:
Cool season grasses, like Kentucky bluegrass, ryegrass, fescue, do well in shaded situations. And in fact, some research shows that they grow earlier in Spring and later in Autmn than when trees are not a part of the system. This is mainly because of the microclimate that is created, which enables forage-able grasses to grow for more days of the year. Warm season grasses are more shade intolerant, but there is variability, so, it's possible to select warm season grasses that could work in shadey situations.
Photo credit: Brett Chedzoy