This was a very good question brought up by a reader of the prior post. As it turns out, deer and elk move between summer and winter ranges. The winter range is at a lower elevation where there are more resources such as shrubs and grasses. Since they eat similar foods, they often compete for resources during the winter when they are more scarce. Since elk are larger and more aggressive, they often win these competitions. According to an article from the University of Idaho, elk are also more tolerant of the cold, can traverse through deeper snow, and use less energy than deer.
University of Idaho