The idea of the steppe - and the human powers within - as a source of danger has largely gone away in the modern era, at least from the perspective of settled societies. For our purposes, we'll expand the idea of the steppe from a land and plains-based concept to a more general concept of an unsettled wilderness hosting nomadic peoples.
In the ancient world you had this fear of the mysterious Sea Peoples in the Bronze Age, who would eventually inundate Eastern Mediterranean settlements in the Bronze Age collapse, possibly due to number of factors including climate change, and then a similar Roman fear of the Germanic tribes. And eventually the Germanic peoples would be pushed in deeper and deeper conflict with the ailing Roman Empire as the Huns put pressure on them from the East, possibly due in part to climate change as well.
The Arab conquerors would emerge out of the deserts of the Middle East to shake the Byzantine and Persian empires at their foundations. And in the Middle Ages you had the conquest of raider societies like the Vikings who were emerging from island colonies and the seas, and then the rise of the Mongol Empire out of the Asian steppes in the East.
Curiously though, in the 15th century as European colonization really took off, you saw the rolling human displacements flip from a steppe phenomenon to a settled society phenomenon. European colonies were not only seen as outposts of wealth extraction, but also outlets to expel underclass peoples and redirect social problems and surplus population and capital outward. There was a constant rolling domino effect in North America for example, as more and more settlers landed on the East coast and fanned out to the West, pushing successive Native American tribes west in turn.
In the era of imperialism and through the modern era itself, much of the pressure was coming from the grinding wars of the constantly expanding empires themselves, steamrolling the nomadic peoples and filling ever more corners of the earth with settled society, with immigrant populations crashing into each other after successive waves of migration. And now the displacements may come back around, as the heating climate pushes the climate refuges to and fro, to temporary regions of lesser destruction.
