There are several organizations that put on competitive trail rides. Each has their own rules and objectives to what is a successful ride. But in general the concept is to promote sound and safe trail horses.
I used to do NATRC (north american trail ride conference) Most of their rides are weekend events. Usually covering 40-50 miles over two days. The offer several classes and divisions. Open, Competitive Pleasure and Novice with Heavyweight, Lightweight and Junior riders.
Think of a comptetitive trail ride like a road ralley. All horses need to travel the same trail, at the same speed, while carrying their rider. They are judged on conditioning and horsemanship skills. They are not a race. A set course will be set up, Maps furnished and a time to achieve the various check points will be set. The rides I participated in allowed a 30 minute window. 15 minutes too early or 15 minutes too late and you were out of the game. So you needed to learn to rate your horses speed to cover the prescribed distance.
Judges will periodically watch you and your horse deal with obsticles. Depending on what is available in your area, These may be be natural obsticles, like crossing a log, climbing a steep hill, crossing water or they may be more contrived such as opening a gate while mounted, sidepassing over and hanging a slicker on a tree.
I found folks at these events to be extremely helpful in helping each other and almost became family after a summer of competing together.
The biggest draw back is finding events in your area. With todays fuel cost, It is hard to justify driving 10 hours to compete. So check with the various organization and see who has events in your general area. www.natrc.org