Well, a lot of them did – the “Redforts, the Hunters, the Coldwaters, the Belmores, and the Royces” are all First Men Houses and gained access to Andal technology when they bent the knee.
But if you’re asking why before: blacksmiths aren’t usually that numerous among raiding expeditions. Learning how to use iron isn’t as simple as just knowing there’s a thing called iron – iron is actually rather difficult to forge, and there’s a whole bunch of interlocking technologies all the way from mining to quenching, that you need to get right.
But no, the First Men absolutely had horses – Robar used his mounted forces to launch his counter-charge against the Andal lines which almost won him the battle. The Andals had more horses, that’s all.