Two more suggestions. Bring headlamps just in case (and make sure the lead horse is used to it). If you are going when there are leaves on the trees, don't go through the woods expecting the moon to light your path!! We went on a Super Moon Ride this summer and since I've ridden by moonlight often, I scoffed at the idea of headlamps. When we hit the woods that we needed to take to get home, it was black as pitch. Thankfully, my horse knows the trail and we are a good team and we all made it back safe. The rest of the ride was wonderful. We started out before sundown so the horses new to night riding had time to adjust.
Even better is riding under a full moon through a snow-dusted landscape - ABSOLUTELY MAGICAL!!!!! As long as you dress warm enough ( :
I used to have a public riding stable, safety being the key to a great time for all levels of riding. The full moon trail rides were my most popular and sold out a month in advance. We had a lead guide with a red reflector lamp turned backwards so the last person in the back of the line could see the front guide and a red light reflector lamp facing forward and the last guide so we could see the last person in the string. We had several guides in the middle of the string so the customers knew we had experienced riders in the group. The horses knew the trail very well. Kickers were at the back with a guide horse behind them. We carried first aid kits for horse and rider, carried flashlights, required the guides to know basic first aid and CPR. Everything was slow and relaxed. No drinking or any risky behavior. It was a great time for everyone.
Several of us that board together watch the moon closely. Almost every full moon, and sometimes not so full moons, we will go on moonlight rides. We will leave the non-horsey husbands to watch the campfire. We go Spring, Summer, Autumn and Winter, as long as it is not below zero or a negative wind chill.