The cowboys I've rode with and the old (very old)timers I know trained their horses pretty much in an ordinary way. They might not have started them until they were 3, 4 or 5, but other than that it isn't anything weird.
Halter break, train to tie and stand tied, get used to the saddle, get on with either a halter, a snaffle or a bosal. One difference is that once the horse could be saddled and knew even a smidgen of turn, go stop, the cowboy then took it out to work all day (or most of a day). They learn quick with so much opportunity.
Because of the age and our colder climate, some may be more prone to buck on a chilly morning, but that's not a deal breaker. After a few long days, they don't waste the energy.
Abuse a horse, then and now, and you get fired very quickly. Horses are part of the team. Why would anyone be allowed to hurt a working partner? It doesn't happen like some publications and clinicians seem to want us to believe.