In many ways the ‘Little Ice Age’ of the late middle ages was similar to the cold period during the late Classical period and the early middle ages. The weather got colder, crops failed, and a terrible plague wiped out much of the population. Perhaps the difference in outcomes was due to the adaptation of new labor saving technology in the West, something that the Romans, with their slave economy, never tried.
The medieval warming may have been even warmer than that of classical Roman times; the cooling may have been even colder.
They did have a lot of slavery, and even more serious was the level of idleness. The bread dole in the city of Rome amounted to feeding as much as 40 per cent of the population at times, and perhaps a couple hundred thousand all the time, for four centuries or more. There’s a classical-era bon mot regarding how the writer had to travel in the provinces to hear Latin spoken, but I’m sure there’s no modern parallel to draw. ;’)
Gaul and Britain took to Romanization very well, as Archie Bunker might say, after the Romans whipped the hell out of them in a war. Estimates of the carnage in Gaul as a consequence of Julius Caesar’s conquest go as high as two million (combat-related death being a small fraction of that). Because it took eight years or whatever, Caesar rounded up large numbers of the population and sold them into slavery in part to defray his campaigning costs and debts (directly through sale of slaves, indirectly by granting slaves to soldiers in lieu of cash), and the groups the Romans called Germans had already crossed the Rhine here and there long before Rome arrived (Caesar remarks on this in the Commentaries).
After the conquest, Gauls and Germans could enter service as auxiliaries (and eventually as regular legionnaries and Praetorian guards) and achieve Roman citizenship, and a good number did. Arminius, leader of the famous revolt against Varus that resulted in the annihilation of three legions east of the Rhine, had served 25 years as an auxiliary and had been granted citizenship. His brother who remained loyal to Rome had done similarly.
Migratory tribes continued to pass westward down the steppes, and arrived in Dacia, and in the various areas of Europe north of the Alps and Danube and east of the Rhine. So much land was available and turning back to forest after the conquest that the Roman presence (which was substantial and went quite deep into areas until recently thought to be strictly barbarian) was a network of roads and towns amid the smallish local settlements by various ethnic groups.
The borders were kept pretty quiet for centuries through trade, bribery to maintain a dependent barbarian ruling class, and cross-border interdictions — all with a relative handful of legions spread across Europe from the North Sea to the Black Sea. By the time the centuries-long trickle became a flood, the Roman military was a shell of its old self, having spent much of the 3rd century engaged in intra-Roman warfare. There was a recovery of central government in the 4th century, about the time migrations by violent raiders and whatnot became a serious problem.
Meanwhile, the Romans had used machinery (even though the smiths et al weren’t high on the social scale) which saved a lot of labor; rediscovery of Roman invention — mills and the like — coincided with the medieval disasters of the Plague and the Little Ice Age famines. Labor was expensive, and the happenstance of classical info trickling in from Constantinople as the Moslems advanced in the east and Spain as they were driven out of the west) and/or greater appreciation of what records had survived actually lead, eventually, to our own industrial society. :’)