Is there any Shut sefer or other that permits a women not covering her hair NOT the Aruch Hashulchan saying it is not Ervah but allowing a women to go out in modern times with their Hair uncovered?
To summarize, Rabbi Yosef Messas (pronounced "Mashash") (born about 100 years ago in Morocco, served as rabbi in Northen Africa and then later in Haifa) allows it in a responsum, Mayim Chaim II OC 110:
Though some claim he was only referring to specific communities, where if he didn't allow it, they would stop keeping Torah, etc.
This is one of the many, many sources cited by Rabbi Michael Broyde in a recent article in Tradition, in which he argues as a limud zechut -- to judge favorably on the many noble women who sacrificed (and still do today) tremendously to keep Torah, shabbos, kashrus, taharas hamishpacha, etc., but did not cover their hair.
Rabbi Broyde argues that the requirement for any hair covering for married women is culturally relative; he has a few acharonim such as the above, plus some readings of Rishonim on various Gemaras to support that view. He then goes further to suggest the Tur and Shulchan Aruch (whose wording on the subject follows the stream-of-consciousness style of the Gemara, not the clear reorganization that Rambam uses) could be read that way as well; on this point, many disagree.