I ride at night often in the summer. Just in the pasture or I sometimes even go out on the trails/roads but no matter what I will ALWAYS have all my high visibility gear on (reflective quartersheet, reflective pastern wraps, and a high-vis vest for me) plus a head lamp, and usually someone with me. And even if I have company I have my phone with me.
You will want high-vis gear no matter where you ride as some people might be out hunting (legally or otherwise) and if you don't have the high-vis stuff they might mistake you for an animal... things can go very badly wrong from there.
I ride at night all the time when it's winter and autumn, but only in the arena. I'd suggest you get a head lamp and go riding only where you know the terrain perfectly.
However, when it has been snowing, I sometimes go even trail riding at night, because the snow lightens everything up, and, if the Moon happens to be shining, it's a winter wonderland I've got here. :) Although some horses tend to be spooked more easily during nights, so you've got to be confident with that, too.
I always ride at night! Especially in the school holidays. It is absoultly fine, because horses have amazing eyesight. I remeber riding the TBs on racetrack once at about 4 in the morning an there was a huge mist, could barely see my hand in front of me yet the trainer made us gallop around the track (me blind), but my horse was fine.
The biggest thing, especially if you have spooky horses, is to NOT RIDE WITH A HEADLIGHT OR TORCH! It creates shadows which are monsters in disguise (according to my horse). Obvisoulsy if you are in a tricky part in a trail breifly shine it ahead to make sure everything is fine, but other than that leave it to your horse.
I'm not sure, I would have to look it up, but there is a huge several day trail ride that some people I know attend and I'm pretty sure that the organization that hosts the events recommends NOT to use a light while riding at night because horses can see pretty well at night on their own and your light can have a negative effect on the night vision of your horse. It makes sense if you think about it. When our barn light is on, and I am standing near it, I can not see past the area that is lit up, but when its off and my eyes have adjusted to the dark, I can actually see much farther out. Obviously, you would want a light in case of an emergency or other problem, but I think actually having a light on while riding would be more problematic for the horse than not having one... just my opinion though until I can find the info to back me up :)
I ride at night all the time and I've never had a single problem with a horse stumbling or stepping wrong even when there is no moon.
However, I would like to echo MadOnNags about properly prepping your horse for the head lamp/flashlight. Most horses get a bit freaked out the first time you use something like that from their back for the reasons already stated. It causes the shadows to jump around and change size suddenly. I don't usually ride with any kind of lamp anyway just because it doesn't really help the horse at all, they are more for my benefit but I have found that if I can't see, I have to focus more on the horse than I would on a normal ride.