A deer’s eyes have photo receptors that give them a wide field of view, but not much focus.
I hear all the time that hunting during a full moon is difficult because it allows the deer to feed more at night (and thus move less in daylight), because they can see better. Think about that for a moment. When it is totally dark, with no moon at all, deer do very well at night. They aren’t out there stumbling around, walking into trees, because they see extremely well in low light. When you walk to your tree stand and it’s totally dark and you bump a deer, it runs off with no problem. No stumbling around, just gone.
Bottom line is that deer do not need the moon to see at night. This isn’t to say that the moon doesn’t affect deer movements, but such movements aren’t related to a deer’s nighttime vision.