> sometimes the stereotypes were the opposite of what they are today.
Correct, and this is the reason for which I qualified my statement. They do, however, apply to the section where western "horse culture" as is being debated arose.
I commented on some of this already, and don't want to pollute the comments too much. Link: https://news.ycombinator.com/item?id=19780759
From what I've read, riding fast horses was much more popular with men before cars.