I've only ridden a couple times. I would suggest something that was meant for a little distance (since you might be at speed), but I don't know how a horse would respond to a hotspot whipping around, especially if it was small. I also wouldn't trust any flashlight clipped to a hat while in a trot. I also don't know if the brightness (for distance) would last very long with an 18350 or single CR123.
I, too, might suggest looking into a headlamp that is secure, has a wide enough beam to see obstacles, holes, buildings?, etc. without having to whip a small hostspot on. Usually floody lights will need a bit more power and juice to get good distance. I might suggest something like the Nitecore HU60 with a belt mounted battery. It has an adjustable beam profile, long lasting battery bank options, and has a remote you can put on your wrist if you don't want to take your hands far off the reins.