Verses with the word horseman in the Old Testament (2 verses):

2 Kings 9:17
And there stood a watchman on the tower in Jezreel, and he spied the company of Jehu as he came, and said, I see a company. And Joram said, Take an horseman, and send to meet them, and let him say, Is it peace?

Nahum 3:3
The horseman lifteth up both the bright sword and the glittering spear: and there is a multitude of slain, and a great number of carcases; and there is none end of their corpses; they stumble upon their corpses: