I've seen antler growth on mule deer bucks in late March after a really mild winter, to as late as late May when the surviving bucks came out of winter in really poor shape. I believe it has to do with replenishing body reserves to a certain level before antler growth starts, but I don't know that it has been shown scientifically - just a guess.
I took care of a well-fed, mature 6pt bull for a couple of years - he would show new antler growth starting less than a week after dropping his antlers. Same facility had several species of deer, all of those bucks (whitetail, fallow, sika, Reeves muntjac, caribou) seemed to have a scab for quite a while, and a bigger gap in time between antler drop and growth.