Deers will eat a variety of nuts and fruits. Among their favorites are apples and persimmon, two fall fruits. However, if available, they’ll just as happily take beech nuts or acorns. Acorns are something of a commodity in the animal kingdom, like chocolate or (even though this is gag worthy) shark fin soup. Pecans and walnuts are also welcomed additions to the humble acorn.
A few staples of the diet of a deer include grass and alfalfa, as well as nuts in general, corn, fungi, and fruit - as mentioned in passing with apples and persimmon. If they can get access to any of these things, they’ll eat them - regardless of if they’re on the side of the road, in your garden, or simply there for the taking.