The California vaquero style of horsemanship NEVER included a snaffle bit phase until recently. They have been effectively used for thousands of years for riding and driving. Of late, they have become part of the south/northwestern cowboy or northwestern buckaroo styles.
In the last hundred plus years, some colts (young horses whether male or female) were started in the snaffle.
This stage has been added by many for several reasons including:
1. facilitating the showing or sale of young horses for someone to continue their education for a job or for future competition,
2. getting young horses under control with some understanding of how to balance a rider and perform basic maneuvers,
3. the re-education of mature, troubled or difficult horses and the need to get a job done,
4. the lack of availability properly made hackamore gear and training in how to use it, and
5. the average rider can ride without the work and education necessary with the hackamore which usually takes longer. This was particularly helpful at the remount stations where the horses and mules needed to be prepared to pull wagons and weapons as well as carry cavalry soldiers with unknown riding backgrounds.
Snaffle bits were looked upon by the old timers as a last resort for troubled horses. The old California saying was that they were thought of as useful for driving horses, easterners and for Englishmen.