Long story short .... buddy of mine and i kept very detailed records for 3 seasons running. We hunt deer in SE Alabama and put in about 60 days each season. I crunched the numbers and found only a moderate correlation between "moon phase" and deer sighting. Here's that one - Clear night + bright moon, deer tended to move later in the day, closer to noonish. Add abnormally warm weather to that combo and its a tough deal when it comes to bagging deer down this way.
For sure weather was the number one influence, and by far.
I never had, nor have since, paid any attention to the moon phase. Deer or no deer, I always have a good day when I am out in the woods.