Riding habit

A riding habit is women's clothing for horseback riding.
Since the mid-17th century, a formal habit for riding sidesaddle usually consisted of:

A tailored jacket with a long skirt to match
A tailored shirt or chemisette
A hat, often in the most formal men's style of the day

Low-heeled boots, gloves, and often a stock tie or cravat complete the ensemble. Typically, throughout the period the riding habit used details from male dress, whether large turned cuffs, gold trims or buttons. The colours were very often darker and more masculine than those on normal clothes. Earlier styles can be similar to the dresses worn by boys before breeching in these respects.
When high waists were the fashion, from roughly 1790 to 1820, the habit could be a coat dress called a riding coat or a petticoat with a short jacket.

Origins

In France in the 17th century, women who rode wore an outfit called a devantiere. The skirt of the devantiere was split up the back to enable astride riding. By the early 19th century, in addition to describing the whole costume, a devantiere could describe any part of the riding habit, be it the skirt, the apron, or the riding coat.
In his diary for June 12, 1666, Samuel Pepys wrote:
Two and a half centuries later, Emily Post would write:

Women's redingote

The redingote is a type of coat that has had several forms over time. The name is derived from a French alteration of the English "riding coat", an example of reborrowing.
The first form of the redingote was in the 18th century, when it was used for travel on horseback. This coat was a bulky, utilitarian garment. It would begin to evolve into a fashionable accessory in the last two decades of the 18th century, when women began wearing a perfectly tailored style of the redingote, which was inspired by men's fashion of the time. Italian fashion also picked it up, adapting it for more formal occasions.
The redingote à la Hussar was trimmed with parallel rows of horizontal braid in the fashion of Hussars' uniforms.
The style continued to evolve through the late 19th century, until it took a form similar to today's redingote. The newer form is marked by a close fit at the chest and waist, a belt, and a flare toward the hem.