Horseback Riding for Women
Once upon a time the camel, horse and donkey were the primary means of transport for both men and women. There are guidelines for men: they may not ride an animal bareback—they are required to use a saddle.
There are guidelines for women, as well: When Torah sources speak of a woman on horseback, she is always “sitting” as opposed to “riding.” The Gemara explains this distinction to mean that riding astride is deemed a breach of tznius (modesty) for women. Traditionally, the side-saddle was the preferred method of travel for modest women in both Jewish and (l’havdil) non-Jewish circles.
In this day and age, when riding is no longer necessary for travel, it is not proper for women to ride in public altogether. Women and girls who wish to go horseback riding for recreation should adhere to the guidelines of tznius (as when engaging in all sports): they should ride side-saddle, in long skirts and in all-female company. (There are a small number of sport clubs in the modern age that support the historical use of side-saddles for women. Someone who wishes to make use of them should research well for possible venues and safety concerns.)