First full moon after the equinox is the harvest moon. The harvest moon was originally named with the farmer's in mind as the full moon gave them enough light to work through the night harvesting their crops. Obviously, this was named long before there were lights on tractors.
Most people refer to the second full moon after the fall equinox as the hunter's moon. Not sure of the origin, but usually falls in the later part of October. This year it actually falls on November 2nd. As you can see this moon cooridnates with colder temp.'s, rut activity, etc... There are some people who believe the moon phase dictates deer movement and hunt religiously by the moon with great success. I am not one of those people.
IMHO: When you have a full moon in the sky, the deer can see better at night. Therefore, they do not have to get up early to make their way to the feeding areas or search for does. Just wait tilll dark as they will still be able to see even better then normal with the moon. Sometimes this can be offset by the colder temp.'s and the deer's search for food. It is rut time, so anytime I get to be in the woods is good, but I usually see more deer with no moon (new moon).