I mean, the Mongols under Genghis were dirt poor in medieval terms initially. The Mongols still had significant numbers of their forces using bone-tipped arrows during the conflict with the Tatars, out of sheer poverty, and doubtlessly some continued using such low-quality missiles into the initial conflicts with the Western Xia and Jin.

Nomads having horses doesn’t mean much; there are far fewer of them on a larger amount of land than sedentary peoples, and high-value goods outside of a functioning and united market economy means very little. It’s one of the reasons why one of the high priorities of early Mongol looting was the enslavement of artisans - they lacked both goods and the expertise (or industrial base) to make them.