I've been asked about my bucket hangers quiet a few times. Every endurance rider uses these, and I am sure they're seen on trailers of every discipline. I have two mounted on each side of my trailer. I use one to hang a five gallon bucket of water, and the other is for the two gallon buckets that I use for feed.
There is a "lip" at the bottom of the bracket on which to hang the edge of the bucket. At the top of the bracket is a small pin that lifts up to hold the bucket handle. Once the handle is inserted, drop the pin back in place and the bucket is held securely. Installation is fairly easy, but you do have to drill through your trailer wall (Yikes!) and it is much sturdier if you can mount it to a trailer "rib" (see inset photo above). Once they're mounted, the bucket hangers are on for good, so pick your spot wisely!
The brackets can be mounted to any flat surface: horse trailer, stall wall, barn wall, etc. Even though I am no longer "racing," I use my bucket hangers every single time I travel. If I go to a lesson or a show, I hang a bucket so that I know my pony can drink if he wants. Speedy expects the water and the feed bucket!