I know there was a type of bow used in the crusades, by the turks against the christians, that was fired with the feet and could rain arrows down upon a target from an incredible range. Something like this may be feasible. Aside from that, screening your main force with light cavalry, light missle cavalry ideally, is really your only option to keep mobile missle armed horse off of your army.
Combating a nomadic society with no major settlements that possess a mounted warfare culture is going to be difficult unless you adopt their tactics. Using heavy infantry against light, fast, mounted archers is going to be futile. If I were a general tasked with invading such lands I would ally myself with various tribes, buying them with whatever they found valuable and using them against my enemy. I would also hire local mercenaries to fight in their fashion. I would attempt to strike at their food supply as well, forcing them to migrate or seek out and attempt to destroy their villages and massacre their women and children until they relented. If you attack something they are forced to defend eventually they'll have to stand and fight and stop the hit and run tactics.
I would only do this if there was something really worth gaining from the lands, and I'd want to be sure I could hold the territory without dealing constantly with marauding nomadic horsemen. Something like a river barrier would work, otherwise I'd have to build some kind of fortification.
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