Misconception: Muslim Women have no Choice, only to cover
As I wrote before, Saudia Arabia is the only country that requires women to cover. Depending on the religion and culture of the society of which a woman lives is a determiner for whether or not she will cover.
I have been told by many women that they choose to cover because of the harrassment that receive from men. While Arab men can be very respectful towards foreigners, it can often be the complete opposite towards an Arab woman. However, this all depends of the country and culture. For example, I have friends who live in Yemen, who wear full headscarf, abeya and naqqab; however, when they travel abroad they often shed all of these coverings. One of my friends is Syrian-Yemeni, while in Yemen she wears abeya and headscarf. But, when she travels to Syria she wears no coverings and goes around in short skirts with her hair flying blowing in the wind.
Before passing judgments on a country...it's religion and culture...be wary that there is indeed a difference between religion and culture. Practices in the Middle East are not all from Islam, they are learned behaviors deep rooted in the regions culture and history.