Our BO will do moonlight rides on nights with a full moon if enough people "buy in" on it or he has a special request from a customer. They do it without lights (except flashlights in case someone needs to potty or whatever) and on rather rocky, mountainous trails and have yet to have anyone injured or any horses injured.
As Darrin said, having "headlights" will kill your night vision and your horse's and would do more harm than good.