I am no biologist, but I have seen this kinda thing happen a few times. In KY where I hunt it isn't uncommon for some bucks to drop the first or second week of Jan. Where you are it gets a bit colder and you have more hard Winters than we do. The only way a buck will drop his head gear is by his testosterone levels dropping. It may be that the rut ended early and most all the does in that area were bred or it may be the stress from a hard Winter then or coming. Some bucks may keep their antlers a bit longer if there are many does in the area, because their senses tell them they may still have to fight to breed. Deer have a keen sense that lets them know ahead of time what to be ready for, it might be bad weather or it may be a second or even a third rut cycle. Anyway, from what I have learned from biologist I know is, the drop in testosterone can be from one of two things, the rut being over or stress regardless of what the stress came from.
To add one more bit of info, if the bucks lacked nutrition or water during the growth stages of antlers, it would show in antlers size as a whole. It would not have an effect on whether or not they drop them early. Unless you have an abstract number of deer in the area, the deer will get what they need to sustain their normal behaver. The only way I see nutrition being a factor is if there were a drought that didn't grow much forage and the mast crop suffered tremendously or the carrying capacity of the area is severely breeched. That would put enough stress on them added to the rut to make them drop early.
Hope this helps.