In my experience it is pretty rare to encounter antlered deer up in the Park; they seem to stay out of sight for the most part. Last year I saw a five year old up at Big Meadow - that was a rack that really stopped traffic, especially since he was in one of the most popular parts of the Park on one of the busiest weekends!
Actually, the Park started closing some sections for hunting season last weekend. As I entered on Saturday afternoon, I was advised that the North District (Front Royal to Thornton Gap) and the South District (Elkton to Waynesboro) would close at five p.m. until daylight
I've learned (and thanks to posumcop for pointing me in the right direction) that these closures are actually to prevent illegal hunting in the Park. There is a link to learn more here: http://www.nps.gov/shen/parknews/park-announces-night-closure-of-the-skyline-drive-during-hunting-season.htm
If you're planning a visit, be sure and check in for potential closings. You don't want to find yourself locked in the Park