RE: does late antler retention = good nutrition?
If by good nutrition you mean in an overall sense a winter with plenty of food and little stress, I would agree. With very hard winters (as ours in IA has been) bucks often loose thier antlers in early january, but other years I have seen many racked bucks as late as mid March. The last antlered deer I have seen was Jan 11th this year....and I have seen many deer since then.
I think all else being equal, providing plenty of nutrious food for the deer would make them keep their racks longer....but deep snow/cold temps would make them loose them earlier, regardless of what they have to eat.