The Ice Houses and Ice Pits in the Middle East and Africa

Ice houses and ice pits pop up in other civilizations. Does it seem like this is a case of cultural transmission or is just kind of like independent inventions from people who have access to snow? If you don't have that access, it's not going to happen. The Apennines was the big source of ice for Rome. As Hovster is in Seville, you still have mountains quite close by where you can get the ice from.