If we’re talking about mass seasonal exodus, then this is an entirely recent phenomenon in southern Europe, post-WW2. So depends on OP’s definition of “old-school”.
Also before WWII. Nomadic tribes have followed the seasons for thousands of years.
And before industrialization, cities were administrative centers and not production centers. The king or ruler and all the elite would go away in the summer to escape the heat, and then there wasn't much reason for everyone else to stay in town. And it didn't cost money to go stay with your relatives in the countryside or seaside. But you'd probably have to help out with farm work.