In researching riding aside, I found that TODAY, many ladies like wearing corsets when they ride! Wow - I always viewed corsets as being binding, tight, restricting and well just plain uncomfortable! At the turn of the 20Th century, ladies knew the standard dress corset would not work for riding - so the Riding Corset was invented.
It's purpose was not to "wasp" the waist, but rather give support to the back and bust, yet allow free movement at the waist and hip. Notice how it flairs away at the bottom.