In short, political expediency, money and prestige of the cultural milieu that they found themselves in, at least that's according to the idea of the book entitled The Steppe and the Sown. Basic idea is that generally steppe peoples may be able to conquer an area, but were numerically much smaller than the people they conquered. Through intermarriage and simple political expediency, the new ruling class would adopt much of the culture of the people they inherited. Areas that were particularly wealthy and seen as advance had the added pull for the assimilation of their conquerors, such as in the case of the nomadic invaders of China, or in the case of the Magyars, their leaders adopted European practices and especially Christianity to legitimize their rule. Why specifically heavily armored cavalry, I cannot say.