I know that Jewish women married to non-Jews do not need to go to mikvah (and indeed should not do so with a blessing). Is there any evidence suggesting that a woman married to a non-Jew does not have to cover her hair, or has a diminished requirement for it?
Motivation: I don't have a very good sense of this, but it would seem (maybe, possibly) that she is not forbidden to other Jewish men if married to a non-Jew...in fact, I'm not even sure to what extent she is considered "married" under Jewish law. Thus she might not need to take on the expanded tznius requirements of a married woman (if we are calling hair covering that). (...This is all just speculation. Feel free to correct.)
EDITED TO ADD:
I'm asking also partially in light of a story of a woman I knew. She was married to a non-Jew, but had begun to take an interest in Yiddishkeit because their 9-year-old son was an extremely serious Jew. Her rebbetzin had her start wearing a hat at a retreat we were at. I found it interesting. I also think we should keep such sensitive cases in mind when we post comments here.
Related: Tznius and B'not Noach