The growth rate isn't affected by sunlight, but the annual initiation of antler growth, calcification of the antler (and velvet shedding), and casting of the antler is. The growth rate, size, and conformation of antlers are controlled by the age of the male, his genetic potential for growth and size of antlers, and nutritional intake that can be devoted to antler growth (meaning if the have an injury or disease, or are still putting a lot of resources into body growth, as young males do, then they won't put as many nutrients and energy into antler growth).