Someone should have paid attention in class.
Whitetail deer (Odocoileus virginianus) are browsers and opportunistic feeders. They do not have upper incisors as true grazers do. They will eat some grasses, but because of the lack of upper incisors, they tend to pull the grass/vegetation out instead of cutting it off as do grazers. The more tender, lower fiber base of the grassy vegetation is preferred by their digestive system over the upper, fibrous, mature part of the grass. Because they can eat the less mature, lower portion of grasses, they will often be found feeding in frequently mowed areas (lawns and golf courses) as well as areas frequented by the true grazers (cow/horse/sheep pastures) which do a similar thing to the grass as mowing does. Whitetail deer cannot live on grass alone as the true grazers can.
That said, some deer, such as axis deer, are more frequent grazers.
Fun Fact: Whitetail deer are herbivores that will eat just about anything they can get in their yap. Some have reportedly been observed eating birds, insects and mice when their typical food sources are low.