All members of the equine family have evolved to extract their necessary nutrition from grasses. Horses and donkeys especially are able to extract nutrients from coarse grasses and plants that might not support a larger horse. Their teeth are suited to grinding the coarse plant fiber, and the long, slow digestive system efficiently extracts nutrients and energy from the plants it eats.
Some horses are easy keepers and are able to live quite well on minimal pastures. Others will be starved for nutrition. A horse that is working very hard may not get enough nutrition. It really depends on the type of horse you have and what its job is as to whether or not it will thrive on a diet of grass, especially one that isn’t top-notch.