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The earliest known type of sidesaddle was a stuffed pillow that was attached to the back of a man's saddle. This was called a "pillion". The lady would have been positioned completely sideways on the horse. There are two short scenes in the movie "The Other Boleyn Girl" of ladies riding pillion.
 Later a saddle was developed that had a foot rest and back rest. Often they also had hand holds in the front and back. Called a "planchette," this would also place the rider sideways.

Views of a Planchette that is over 400 years old
Two more Planchettes
the left one was made by Jami Wormer
It is unknown when the upright horn, the one the rider hooks her right leg around, came into use.
Delcared to be a 16th century saddle -
could this be an early upright horn?
The second horn, an appendage that comes from the right side of the saddle, is commonly attributed to Catherine de Medici. This would cradle the right leg between the two horns and offered a bit more security.

This saddle is later than the 1500's but shows the second horn (not to be confused with the leaping horn).  The saddle also shows the rigging used for Western saddles.
Early in this century, the leaping horn was invented. Both the French and English lay claim to this advancement. It was also at this time that the balance strap was created. This strap is attached to the right rear of the saddle, passed under the belly of the horse, and fastened to the left front. This served to stabilize the saddle and offset the extra weight from both legs being on the left side of the horse.
The Victorian era in the late 1800s was during the reign of Queen Victoria and is typically what we think of when we recall "sidesaddle". Queen Victoria wore black for much of her life in memory of her late husband and the ladies of the day emulated her. Could this be the nexus of the traditional black habit seen in the hunt field? A lady's horse was trained to walk and do a collected canter. It was unseemly for a lady to be bouncing at the trot. Riders were quite often sewn into their habits in order to show off their figure to best advantage.

Queen Elizabeth I's sidesaddle
In the 1860s, a western sidesaddle was attributed to Charles Goodnight from the United States. He had a saddle made for his wife, built on a western-style tree. It was believed that the typical English saddle was not sturdy enough for the rough country out west. There are photos of Belle Starr (a notorious bandit and horse thief) on her sidesaddle, usually with her six-gun on her hip. Her saddle is believed to pre-date the Goodnight saddle.
The western sidesaddle often included a "purse" on the offside to hold the lady's incidentals such as coins for tolls, a handkerchief, and, possibly, a small derringer for protection.

"Goodnight" style saddles
Mrs Goodnight
Modern saddles
Habits and Costumes
Queen Victoria's sidesaddle
Some famous ladies who rode sidesaddle include Queen Elizabeth I, Queen Victoria, and today's Queen Elizabeth II. Other riders include Laura Ingles Wilder of "Little House on the Prairie" fame, Annie Oakley, and Sybil Luddington, who rode to warn of the British coming just like Paul Revere, except that she rode further and she didn't get caught!
Queen Elizabeth I

Queen Victoria
The young Queen Mum
Queen Elizabeth II
Emma Hickock
the "Queen of Sidesaddle"
Sybil Luddington
Annie Oakley
Belle Shirley Starr