Like all other germanic Barbarians the Goths were primarily infantry-based, their stay on the Ukranian steppe had probably heightened their proportion of cavalry to infantry, but they were nonetheless still mostly infantry. It is a question of settled farmers being mostly infantry while nomads/herdsmen are primarily cavalry in that specific setting. Battle of Hadrianopolis was an infantry action until the Goth cavalry with their Alan friends/allies/mercenaries returned from foraging and turned the Roman flank. Nor were the Goths the only tribe to invade the WRE and the others were by and large infantry.
Note that at Tours October 10, 732, the well-trained, armed and disciplined Frankish FOOT soldiers withstood the heavy cavalry of the Umayyads and defeated it. Well-trained, armed and disciplined heavy foot will as a general rule defeat any cavalry you care to mention. It is when they break rank as at Hastings, they get slaughtered.
However, it generally takes an organised state to arm, produce and train this body of foot. A state that was by and large absent in the middle ages. Instead the small bands of well equipped and trained cavalry dominated all battlefields where they did not meet organised heavy foot. It is easier to maintain a single or a few knights and bring them together in effective if disorganised and undisciplined warbands than to keep heavy foot (not to mention chivalric ideals and general ideology). In that light some military historians have seen The Middle Ages not so much as the age of cavalry as the age of absent foot.
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