I think along the same lines as Cochise - game will feed more under a full moon and not be so active the following day. That said, the 2 elk hunts and 1 mulie hunt I've been on were without regard to the moon phase. Not gonna give up a chance to hunt just because the 'heavenly bodies weren't in alignment'. Also, my deer was taken at sunrise about 1/2 hour after the moon set! What I 'believe' and what I act on don't always agree.
I also believe that when it's real windy like the past day or so, game will tend not to move around much. I think because the wind noise makes them nervous, they can't discriminate threats as well. My thoughts only, ymmv.