Luckily the history of riding is rather well-documented. We know how useful horses were for pulling carts or wagons from place to place bringing people and produce. We know that they were extensively used in battle. How else can you move an army quickly? We don't know who the first brave soul was to ride a horse, but this was the catalyst for making a crazy feat become the most common mode of transportation in the world before the Industrial Revolution.
Since that initial person, training and riding horses is nothing new. There is a lot of information at one's fingertips now, but here's the truth: it's being reinvented not invented. The basic tenets of riding are the same for any discipline. This is what classical riding is all about. Have you read Centered Riding by Sally Swift? That information is applicable to all disciplines of riding. The importance of balance is just as important to a jumper rider as to a reiner. The aids you are taught or just figured out on your own work the same way for every other horse. It's not a mystery. It's all been learned and done before. But it would be a perfect world if we all learned from history.
"'Classical' means begin with a classic seat. In my [George Morris] view, such a seat must be a versatile one, one which can enable a rider to have a comfortable hack through the country, go fox-hunting, show a hunter, or ride in a hunter seat equitation class, a dressage test (with a longer stirrup), or an open jumper class (with a shorter stirrup). With this seat, the rider should be safe, secure have good style, and - most important of all - be versatile. He should be able to ride any kind of horse, help his horse when necessary, and show him to his best advantage. Only through searching for this all around style can a rider assure himself of complete riding enjoyment and have access to all the many aspects and variety of the sport." George Morris, 1990.
I feel that dressage is classical riding. The more one knows, or feels, about riding, the happier the relationship is between horse and rider. Sitting in balance. understanding lateral work, extending a stride or collecting a stride are basics of any discipline. Riders can do this in any saddle (especially bareback). Try not to pigeon-hole yourself in to only one discipline. Try one or two others. There are more similarities than differences (minus the attire). Think about it this way, football players hone their skills on the field by taking ballet lessons!. So if you'd like to become a better barrel racer, try some dressage lessons. You might be pleasantly surprised.