Iraqis do not typically wear hats; in fact most Iraqi men do not wear anything on their heads at all, similar to most Westerners. Historically, Iraqi men wore fezzes, but this has not been the case for over a hundred years now.
If the question is asking about the cloth that some of the older Iraqi men wear, this is called a kufiyeh (كوفية). In Iraq, the kufiyehs are typically red and white, whereas in the Levant they are black and white.
Some men in the Iraqi military wear berets and other sorts of military hats, but this is part of the uniform and not a personal choice.
Most women in Iraq wear the hijaab, which suffices for their headcovering.
A magic hat
really ugly hat
Sombrero ___~___
He wore a Bowler hat.
a beret
a tam
i will wear the hat!
Wear my Hat
You can wear any hat.
The hat they wear is called a fedora.
Hat
Most Iraqis wear Western attire with men wearing shirts, jeans, and leather jackets, and women wearing shirts and dresses. However, Iraqis tend to wear clothes with dark and muted colors, like black, brown, and navy blue.Older or more traditional Iraqi men will wear the thowb (ثوب) and more traditional Iraqi women will wear the jilbab (جلباب).