It might have been normal but people are people and would still seek out more comfortable climates. And if you stretch the definition of air conditioning a bit, we've had that for about as long as we've been living in semi enclosed spaces. Running a fire at night to keep the cave warm is air conditioning. Building your home to have water flowing under the floors so that you can cool or heat the floors passively (I believe the Romans were doing this) is air conditioning. Hanging a wet towel to allow the water to evaporate and cool the room a little is air conditioning.
Arable land and climates comfortable for people tended to have a very large overlap until the the invention of modern irrigation techniques like center-pivot irrigation. Before that, you need pretty special conditions to be able to successfully farm in many of the places in discussion.
Arable land that isn't habitable for weeks or months out of the year wasn't terribly valuable or sought out.