Lots of good and accurate info here. White-tail are mostly browsers and less grazers: 70:30 and it is the reverse for elk.
Our season starts in September and goes through mid-January. They are in hayfields early, they love alfalfa, timothy, and clovers. They browse new woody shoots as many have pointed out above. In a drought year (2010 here) the persimmons are dropping early but normally after the oak acorns. Enough has been written about white acorns vs. red oaks. The reds are year after year producers, the whites usually are alternate years, at least for bumper crops. Very easy to tell the white and red families apart.
By late season, when the acorns are gone; thank-you deer, turkey, squirrels, and exotic hogs, they go primarily to twigs and certain leaves (exotic honeysuckle, green briar, others mentioned above). By the way dogwood leaves have higher calcium levels -- good for antler growth.
Of course those who live with urban and suburban deer know deer also love; tulips, white cedar, and the fruit trees listed above.
Of course hickory and walnut are useless to deer except they distract the squirrels a bit.