AZ and TexasCountryWoman are exactly right. Cattle are grazers, deer are browsers. The deer's natural diet is forbs (weeds) and brushy type plants. Deer also eat some grass, of course. Check out most oat patches in the fall. But this amounts to only a small part of their total intake.
For their digestive system to work correctly, they must eat a large percentage of fibrous roughage. That's why you will see a deer standing knee deep in grass nibbling the leaves off a yaupon bush. Deer are also edge animals that relate to boundaries where the habitat changes, from brush to meadow, for example.