I actually read a hunting story several years ago and the guy was trying to shoot this one particlar buck. When it did finally present the shot it was in this same state. One antler had already dropped. He shot the buck and spent several days looking for the dropped antler and did find it.
I know the odds would be stacked against me but, with snow on the ground I'd try the same feat. I'd backtrack him to his bedding / feeding areas and hope to find the other antler. If not, I'll eat good.