The Romans had been fighting against steppe cultures and horse archers for centuries. On the Danube frontier, Rome had interactions with the Sarmatians and Scythians (though we should be careful about how Romans labelled tribes and peoples with umbrella names, as many "Scythians" were actually Germanic).

More to the point, however, is the extensive experience in fighting against the Parthians and Sasanians, notably the disastrous Battle of Carrhae in 53BC. The Romans, under Crassus, were hopelessly defeated by the Parthians, who outranged their infantry-based opponents with horse archers, resupplied from camels between engagements, and continually harassing the Romans and inflicting many wounds to the Romans, who could not counter in any way. The knowledge of the "Parthian shot" - the act of shooting at a target when riding away - comes from this conflict. The Parthians would rotate between horse archers and heavy cataphract charges to exploit the immobility of the Roman formations.

Knowledge of this style of warfare was not lost. Mark Antony's campaign against Parthia started with the invasion under Ventidius, who deployed successful counters against the Parthians. At the Cilician Gates (39BC), the Romans held position on the slopes of a hill, and the Parthians charged uphill. The Roman infantry maintained their testudo to protect against Parthian horse archers, and under the cover of missile fire from their own slingers and javelins, the Romans charged downhill and engaged the light Parthian horse archers and routed them. At the Amanus Pass shortly after, the Romans defeated the Parthians again, this time by feigning a cavalry retreat and luring the Parthian a cavalry through the narrow pass and surrounding them.

While the Parthian Wars ended in a stalemate, the Romans were well aware of what light horse archers could do, and knew how to effectively fight against them. Add another hundred or so years of warfare against the Sasanians too.

So, did the Hunnic style of warfare shock the Romans? Probably not.

By the 5th century AD, not only had the Romans fought extensively with eastern kingdoms, their immediate encounters with the Huns gave them much experience. The Roman commander Aetius himself was a hostage under Uldin of the Huns, where he learned much about their way of warfare. Aetius would command mercenary Hunnic warriors in his campaigns in the Western Roman Empire.

The dominance of the Huns during this time isn't necessarily attributed to their superior warfare. Rome was a different empire - split into two, with the West in decline, large regions being taken by migrating tribes displaced by the Huns, the Vandals taking over the African provinces, the Visigoths sacking Rome. In the East, the Sasanians were engaged in war, and the Eastern empire was coming off the back of the Gothic Wars, including the disastrous Battle of Adrianapole. The Huns came and raided large areas of Thracia without opposition. When they did fight against the Romans, the Romans were greatly outnumbered and outmatched, though in general conflict was minimalised through the large tributes paid to the Huns.

The decisive battle between Rome and its allies against the Huns, the Catalaunian Plains in 451AD, saw Aetius effectively fight against Atilla's Huns. The shield walls and foot archers were able to repel the Hunnic horse archers, and counter-attacks by cavalry routed them.

To conclude: What made the Huns so dangerous? In short, there were LOTS of them coming down at a time when the Romans were divided, engaged in internal and external conflicts elsewhere, and also dealing with the migrations of other tribes displaced by the Huns. The mobile style of warfare the Huns specialised in was useful for raids, but in pitched battle did not afford them a significant advantage.