Dressage is a discipline of equestrian sport that focuses on training the horse to respond to subtle aids from the rider. In dressage, horses are trained to have a distinct "working side" - meaning that their mane and tail are typically left on the left side. This allows the rider to maintain a consistent connection with the horse's body, regardless of which rein is being used.
However, it's important to note that the mane on the left isn't specific to dressage alone. Some other disciplines, like show jumping, can also have horses with their mane on the left side, but it's not always mandatory.
Do you have other details about the riding style you're curious about? Maybe you remember other aspects of the rider's attire or the type of horse they were riding. Providing more information would help me identify it more precisely!