Deer, like all ruminants need protein. The bugs in the ruminant are feeding off the carbohydrates and cellulose in the plant material and a nitrogen source and this usually comes from proteins. You can keep ruminants reasonably healthy on ammonia treated straw, or even ammonia treated newspaper - so long as there is of 15% nitrogen to carbon (carbohydrate or cellulose) the animals will do reasonably well.
In the spring time there is plenty of protein in young leaves of grass and bushes, but in the depths of winter all you are left with is cellulose type material ( dried dead grass), and low quality green stuff. Add a bit of protein and this can actually a good maintenance diet, hence munching a dead animal, or seeds and nuts, fungi, lichens etc - all of which are high in nitrogen.
Same happens in the tropics where in the midst of the dry season high nitrogen seed pods, such as acacia are incredibly important in allowing animals to survive. Take away the acacia trees, and whole bush becomes unproductive.