I find this interesting, as although I'm only an occasional stalker, I am out at night after fox and Rabbit very regularly, regardless of weather and moon phase, and my observations regarding Deer (Roe) would suggest that they prefer to be out in the open more during the darker nights.
I almost always see more out in the fields feeding and resting, on the darker, moonless nights than when there's moonlight. They also seem to be far less easily spooked on the darker nights too.
It'd be interesting to hear whether anyone else has noticed similar behaviour, or is it just me?