Only the very wealthy would have pools. The most common form of 'traditional air conditionining' in The Gulf was the wind tower.

An open sided tower was built on the roof. It had walls going diagonally across the inside (at 45%). These walls would catch whatever wind there was, from whichever direction it was blowing, and it would be directed down through a hole in the roof to cool the room or rooms below. Here's one

Bert.