They weren’t like modern sidesaddles at all.
A Spanish sidesaddle from the 14th or 15th century. Photo from Georgia Ladies Aside.
“Then her brother gave the reins of her horse to the childe, who took them and led them to the palace.” – Chapter 78.
Time and again we’ve read in Amadis of Gaul how some knight or nobleman takes the reins of a woman’s horse as they ride along. Is that mere chivalry? No.
As you probably know, women rode sidesaddle in the Middle Ages, but sidesaddles then weren’t like sidesaddles now. Modern sidesaddles have a pair of pommels, which are sort of like curved horns, that women can brace their legs around or against, as well as safety stirrups and other improvements. These allow women to jump fences and gallop safely.
Medieval sidesaddles weren’t exactly chairs mounted sideways on the horse, but that’s what they amounted to. The rider sat in a pillion or padded seat, and her feet rested on a planchette or footrest. A woman didn’t face the direction her horse was going, she sat perpendicular. And she didn’t sit especially securely.
That’s why they rode palfreys. A palfrey isn’t a breed of horse but rather a kind of horse, a lighter-weight animal with a smooth, ambling gait. This is much easier for the rider, and women had to avoid jolts.
So when a man takes a woman’s reins, he’s doing it because someone has to lead her horse. The woman is in no position to do so herself.