I've read the history of reining. The NRHA was formed in 1966, not 1866. What is the purpose of reining? "Reining is a judged event designed to show the athletic ability of a ranch type horse within the confines of a show arena." NRHA - National Reining Horse Association
It isn't wrong, but arena sports do not define western riding. Ranch work does. And many cowboys, when they need to go from point A to point B in an expeditious fashion, post on a trotting horse. Not all do, but posting is not just a training event for arena sports.
Trail riding, like much of ranch riding, involves going from one place to another in the boonies. That is a more realistic sample of ranch work than spinning a horse 360 deg around on its haunches, racing barrels or a WP gait. It isn't the end all of western riding, but it is certainly a type of western riding and just as valid as any arena sport. You don't need to have a judge watching you to be doing western riding.