I often avoid playing established characters during a new moon because it really seems like luck is adversely affected. Monsters seem to be spawned much more rapidly, in greater quantities, stronger, faster, more dangerous, and suspiciously ready to hit me where I'm weakest.(for example, this post was prompted by this event--I had just acquired 18 unidentified potions via my pets cleaning out a liquor store and was on my way to my stash/altar camp to ID them when suddenly a pack of winter wolves was generated. By the time I finished with them, nearly a dozen potions had shattered). Is this just a skewed perception? What exactly does a new moon do?
Other than a message when you start the game & an increased chance of stoning, the New Moon has no other effects. Playing at Night (10PM - 6AM) is actually more dangerous.