From my understanding of Whitetails, their shedding of antlers is somewhat localized based on several factors, those of which that include; stress, nutrition, and new growth. Of course mule deer and elk are different but I would guess they follow a similar pattern.
For example; a perfectly healthy deer "should" not drop their current set of antlers until their new ones are starting to grow. Rut stress, winter stress, predator stress and poor nutrition could cause them to drop early. I would also guess localized genetics could cause them to shed early/later as well.
I usually do not find sheds until late March, but I have seen them shed as early as late Dec and as late as June.