I believe that weather plays a much bigger role in effecting deer movement. I don't discount the moon's effects. Ask a policeman or emergency room doctor. They will verify the moons effects on people. So why not other animals.
Here is another interesting obsevation. The deer must be effected by something because have you ever noticed that when the deer are on the move you see them everywhere. when their not you don't see many. Its like they somehow coordinate their movement times. Since they don't have phones or the internet something must be coordinating their movement.