Probably more or less like the people who inspired them, the nomadic horse archers of the Steppe(Specifically Greek interactions with people groups like the sarmatians). Not being able to get to the ground as easily might make it hard for them to really build things, but in time through trade they would become unparalleled horse archers. Political interactions with humanity at large would probably be rather ossified - either fear, hate, or outright worship would dominate the scene. Centaurs would never be able to create an empire in the style of the Mongols - since they cannot as easily rely on stealth, scale walls, or even enter certain houses, but they would still be feared. Perhaps they would develop a mercenary culture.

They would likely not adapt well to an industrialized culture, and either become marginalized or extinct entirely.