Final answer:
The concept of horse breeds in Houyhnhnm society is a fictional construct from Jonathan Swift's 'Gulliver's Travels,' where the Houyhnhnms are intelligent horses living in an idealized rational society, unlike the human world. There is no mention of different horse breeds within Houyhnhnm society in the novel.
Step-by-step explanation:
The question refers to the role horse breeds have in "Houyhnhnm society," which is a fictional society from Jonathan Swift's satirical novel Gulliver's Travels. Houyhnhnms are a race of intelligent horses, and they represent an ideal of rationality in the novel.
In their society, horse breeds do not play a role as such since Houyhnhnms are depicted as a uniform group, without the emphasis on breeds as found in human societies. Instead, their society is juxtaposed with the corrupt and irrational human society represented by the Yahoos.
The question seems to be a mix-up with real-world horse history and the fictional account, where horses influenced cultures and civilizations such as Native Americans, European nobilities, and the Warring States period in China.