I don't think there are any real mounted archer armies in Europe prior to the Huns, and perhaps not even the Huns qualify
Basically, no Barbarian army is only cavalry-based, and the ratio may even be lesser than for Romans.
For exemple, at Adrianople, the ratio is maybe 1/3 for Romans, while, as for Goths...
Robert Eisenberg said:
However, while the size of the Gothic army can be established at 12,000-15,000 soldiers, its composition must still be explored. While Ammianus’ account credits the Gothic victory to their overwhelming cavalry,
modern scholars believe that it was unlikely that Gothic cavalry was very large, due to the increased pressure on supplies needed to maintain horses, as well as the legitimate point that the Romans would not have allowed
the Goths to keep many horses upon their admittance into the empire.
Also, it seems likely that the Goths would have sold whatever horses they had been allowed to keep for food during the famine in 376. Thus, the Gothic cavalry can be realistically estimated to have numbered no more than 3,000-4,000.
As for Franks, the use of cavalry is largely due to influence of Roman military, whom "cavalrisation" is itself due to Sarmatic/German influences in the IInd to IIIrd centuries.
Huns are often depicted as some Late Antiquity version of Mongols, but...
Well, first, Hunnic hegemony gathered a lot of peoples, and Huns propers were the minority (25% at best). The rest was including Goths, Franks, Herulii, Burgundians, etc.
What we identify as Hunnic warfare was eventually pretty close to the usual German warfare, hugely influenced by Sarmatians and Romans uses. (And even for Huns proper, it's actually not that easy to make a radical distinction between Sarmatians and Huns in part of the equipment in tombs).
While Huns may had more access to cavalry (which doesn't means cavalry-dominated, see below), it's more certain by the Late Antiquity situation, once they're reduced to Danubian and Black Sea coasts : Strategikon advices to attack them in winter, to prevent them using efficiently their cavalry (while, at this point, Huns may have been "Avarized" or plainly Avars, Byzantines being known to use "Huns" for unrelated peoples). But there's nothing to wholly disprove a more important cavalry among Huns proper (even if they're known to be not predominantly so).
But that Hunnic armies, once including their subjects (they lost by the mid Vth) were predominantly or even largely cavalry-based? That can't really be sustained, neither supported.
What does this suggest to me? Well, it suggests the migration-era Germans got more cavalry as a result of their increasing strategic and political sophistication.
Essentially trough their entry in Romania, where influence of a Roman army (itself more cavalry based, would it be only trough more ressources avaible), and with the constitution of Romano-Barbarian hegemonies, using both Roman/Romanized troops and more cavalry-based peoples (as Alans).
But if there is a thing that's as close to a superweapon as can be in the period, heavy cavalry is it.
As was demonstrated by the Battle of Chalons : it's a weapon hard to master (again, Goths had a really limited cavalry at Adrianople, contrary to Romans, but the latter were defeated,
altough for political/structural problems rather than strategical, strictly speaking), but that can pressure efficiently.