I have killed a couple deer not long after first light following a clear full moonlit night in 25+ years of hunting. However, MOST of the time, the MORNING following a full moon yields few if any sightings--and those are very early. The rut is the exception to this "rule" IMO and I killed a nice 8 point a few years ago in the morning after a full moon because he was grunting along behind a doe. Evenings--at least where I hunt - can be as good or even BETTER at this time. I feel that is because the deer are hungry after bedding down so early and are eager to begin feeding again.