Three examples from the First Age [Aman, Middle-earth]
We know that in Aman, Orome had great horses shod with gold, according to The Lay of Leithian.
And Fingon rode against Glauring "with archers on horseback, and hemmed him round with a ring of swift riders" Of The Return of the Noldor
Or in Gondolin, Tuor sees Elven captains and chieftains upon horses, white and grey.
Second Age [Numenor, Middle-earth]
"In Numenor all journeyed from place to place on horseback; for in riding the Numenoreans, both Men and women, took delight, and all the people of the land loved horses." A Description of Numenor
Of Dwarves And Men relates that "in these ways" the Alliance of Dwarves and Men in the North came early in the Second Age -- one of the ways being that Men were tamers of beasts and had learned the mastery of horses, using them for scouting and employing horsed archers against the orks.
Not every example from the legends and stories of course, but some.