Oh I misunderstood what you meant by Roman Cossacks. I think the Byzantines already trained Greek horse archers, along with hiring Pecheneg + Cuman mercenary horse archers of course. And the Byzantines didn't really have that many more technologies than the earlier Romans, who themselves hired Alan horse archer foederati.
So it is possible for Romans to become dedicated horse archers as well as utilize them.
However fully adopting the lifestyle of a nomadic horsemen, rather than just being a cavalryman in the Roman army, is the hard part. Roman Cossacks might have to be prisoners or exiles at first, or perhaps they started as a different ethnic group to Romans but assimilated to Romanity later. Otherwise, if they were Roman citizens, they'd be living with other Roman army units for some temporary (if extended) military service and paid by the Romans, or ruling over some land in the Byzantine Empire, rather than forming a separated frontier state like the Zaparozhian Host.
Also lack of gunpowder/guns makes it a bit harder to train new Cossacks.
No bother - discussion boards are for discussion, no?
So, fundamentally, easy to have the skills - but not to have the people. Forgive the abuse of Faux-Greek and Tolkien, but you could have
Hippo-Dynatoi / Horse-Lords. Basically Roman lords given control over the steppe after victory by a large cavalry arm. Sure they'd have landholders that were farmers near rivers, and like the Zaparozhian Sich, they'd have their main base near those rivers too. At least, that is how I see them emerging - and whilst there may be a lord whose house is based there, I can imagine his sons and most of his men would have to live like Steppe nomads to realistically control their territories, as in order to entice nobles to rule they'd have to have vast tracts of land - and as such they'd need to be able to patrol and defend it, and as much as I like the
skutatoi or
mavros pyritida skutatoi, you're gonna need fast, mobile forces. At least they'd be able to master defence-in-depth!
Aye. Gunpowder would make it easier, especially once it feasibly develops into saddleguns or carbine-style weapons.
@Admiral Beez - I think its pretty fair to assume a post-adoption of the stirrup reality for any of this to work

So we're looking Post-Avars.