My teaching was to always have the mane on the right side of neck, Western horse or English horse, Driving horse, all disciplines. Tradition was developed from the Military system, training of mounted men, requirements of keeping troops of horses so they are alike.
Soldiers are supposed to all be alike. Systems are developed to create uniformity in methods of doing everything. They mount from the left side to avoid tangling leg in sword hung on left hip. Mounting from the left means left hand on neck, holding reins, while right hand adjusts stirrup for foot. Mane on left side will be a problem in tangling hands and reins during mounting. Tangles mean soldier can lose control of animal while unsteady in mounting.
These soldiers were trained in doing things alike, by men trained the same way. Habits, training of years went with these ex-soldiers when they left the military. Kept grooming manes onto right side of neck so they didn’t tangle with reins in mounting. Kept mounting on left side of horse. Trained their children in the same methods.
In the early West, up to the 1960’s, many horse manes were kept roached off, hogged necks for Eastern folks. No mane made roping, rein tangling impossible. Most Western horses had fairly short tails, cut off or pulled so they didn’t get tangled in things. Check out some old photos. Short manes and tails also kept chances of lice down. One lousy horse could easily spread lice thru the herd. This roaching was also seen in the Western Calvary units, no manes at all. Sure reduced care time in grooming of horses too.
After the 1960’s, Western Halter horses, show horses, got more popular, were traveling in trailers to more shows, rodeos. A couple winners had manes, so the style was copied, got more common. With horses often doing multiple jobs, short manes were trained right again, to keep it out of the way when mounting. Old Horse Care Books I read, said to train the mane right, so this was the accepted practice, wide spread and promoted.
Traditionally, driven carriage horses were never braided in daily use, neither manes nor tails. Modern CDE Competition drivers braid manes, but it is a modern choice. Neither required or encouraged. Looks nice, same reason other English disciplines braid their animals. Drafts do braid for their competitions, emphasizes the heavy, muscular neck, power of horse.
Can you do some of the more obscure braids, Hackney braids, Cleveland Bay braids? Used only on these breeds, though they are attractive styles.