And you recruit them through the Military screen? like retinues?
Yes, you do. Also be aware that you can recruit other unit types (and also build certain buildings) depending on the terrain of your capital such as Desert enabling Camels and Jungle enabling Elephants. Every once in awhile you'll have the option to "pack up" your capital and choose a new location.
Pretty much the other big mechanic with Horse Lords is the idea that number of holding slots = manpower. Give the worst provinces with few holding slots to your clans (clan land demand can be seen in the Clans screen) and then keep the best for yourself. Also, de jure is meaningless so you can give out the land any way you want.
Besides that, succession is similar to what the Muslims have- with the difference being that it's basically "Agnatic Prestige". Earn prestige via normal methods, or alternatively you can send sons and relatives off to be mercenaries. Be aware that they can come back as a different religion, which will strain relations with othe clans but can of course offer some interesting advantages. Islam especially is excellent as a horde, since decadence is disabled.