First, in order to understand the implications of Degas’ portrayals of the relationship between horse and rider, it is necessary to understand the context of Degas’ relationship with the horse, specifically why he was so infatuated with is grace and power. This attraction seemed to have developed in adulthood: there is evidence to suggest that Degas had only minimal interaction with horses in his childhood, and he had no known attachment to riding (Kendall, 581). Yet from his earliest training as an artist, he depicted horses as Degas first attempts at drawing horses were made at the Ecole des Beaux-Arts, an art academy in Paris. These early renderings of horses and riders are studies of antiquity, mostly plaster casts from the Parthenon (Boggs, 17-18), making it unsurprising that when studying in Rome he started to depict horses more frequently in his own original works (Lipton, 31). Commenting on why Degas was so interested with horses, the critic Paul Lafond has said, “He loved the horse for its elegance, its fine, spirited high strung bearing, and admired its nobility” (Bouret, 46). As Bouret suggests, Degas admired the horse not only for its elegance but also for its “spirit”, and this “spirit” is what led him to depict the animal in so many of his early works. 
To Degas, the horse was an almost god-like creature, a belief reflected in the many sonnets he wrote about the animal. He wrote, “Pure bred…strong and sound…the brave colt, galloping, cuts through the dew…precocious, impervious” (qtd. Degas, 137). As Degas’ own words suggest, he held the horse in the highest esteem. To him, it was “brave”, “impervious”, and majestic, and as such was far above subservience to man.
Images (top to bottom):
Degas, Copy after the horse in Anthony van Dyck, Charles V, 1858-1859. Bibliotheque Nationale, Paris.
Degas, Riderless Horses (Barberi) in Rome, 1856-1857. The Pierpont Morgan Library, New York.