I have read studies done regarding deer activities during full moon phases, The studies were done by Charles Alsheimer,
He wrote a book titled
"Hunting Whitetails by the Moon"
From what I remember, during a full moon Deer feed all night long and rest/sleep a lot during the following daylight hours.
hunting pressure will get the deer up and moving but if the woods are quiet, I wouldnt expect to see a lot of deer browsing the day after a full moon.