Except that predators also see better at night, thus, they harass deer more during fullmoon light nights. And,studies show, that deer are more active during the week of the full moon during the day (full moon with no clouds at night) than during other moon phases. At least three scientific studies that I know of (including my own 10 year research project, a 3 year study from Georgia, and a 2 year study from Texas) show that.
But, deer activitymay be less during the morning and evening during the full moon, becuse of the increased light, which may make them nervous. Deer generally avoid bright light situations - which is why they move atdawn and dusk.