Rebecca, a fellow blogger and horse lover, sent me a link to a Craiglist ad for an antique side saddle. I saved the photo (as Craiglist listings tend to come and go quickly) because it's an interesting example of a mid 19th century side saddle.
The wide flap would have protected the very full skirts of mid 19th century riding habits, but the deep dipped narrow seat and little skinny upright pommel doesn't look very comfortable. Look how far the safe extends towards the front too. It's hard to tell from the grainy photo, but there looks like there is embroidery or embossing on the safe as well.
At first I thought maybe the sheepskin was added on at a later date to the seat but upon closer inspection, it looks like that is moth eaten as well. I wonder if it is a period addition in an attempt to make the dipped, narrow seat a bit more comfortable.
You can just see a small off-side pommel which were often used as a "hand rest" if you needed some extra security riding these slick saddles with no leaping horns. Ladies wouldn't have done anything adventurous in these types of saddles due to the lack of leaping horn and dipped seats. They are often referred to now as "catalog saddles" as they were sold fairly cheap and ready to go from the mail order catalogs of the time. If you wanted a leaping head on them, you had to pay extra so these saddles are often found without them. This is why catalog saddles seem to survive in great numbers as they were pretty much unrideable except perhaps for walking to church on a Sunday and back again!