Someone may come along shortly and answer your question more scientifically than I can. In short, no, the genetics of an animal are not influenced by food. Food can ensure an animal reaches their full potential but it won't change his genetics.

What can have an effect on genetics is the theory of natural selection, basically "survival of the fittest". The deer in the Midwest are subject to harsher winters than we have here. Basically, the theory of natural selection would indicate that the smaller, weaker deer are killed off. Over time, this means most of the deer that live in these areas come from the deer that were bigger, healthier, and more adaptable to surviving those climates.