While not the Middle East, I spent some time in Sudan along the Nile in the winter. A leather jacket was great at night and early morning. Once the sun comes up, no way. In Tunis, everybody wears leather in the winter and spring. It can be cool and windy near the water. A good jacket is completely appropriate if you are out in the elements, especially to block the wind and sand.
East Africa is completely different climate from the Gulf.