What cows and goats eat?

Goats can and quite often do eat grass just like cows do. Cows will eat leaves as well: grass is pretty much all leaf anyway, but cows will eat leaves off of forbs, trees and shrubs as much as possible or as high as they reach. However, goats are not roughage grazers, rather they are what are called "selective grazers" like deer are, meaning they like or choose to eat leaves from forbs and shrubs than grass.