I'm still wondering about the question of covering your hair outside of liturgy. It sounds like the original question isn't about just putting a hat on but totally covering your hair when you are out living your life. One one level it is good to be more modest than what is presently the norm. But, does it really help you in any way towards living your faith? It sounds like it could be a private devotion, but aren't there other ways of being modest, such as not wearing makeup, etc? Is it ok to wear makeup and still cover your hair?
I had Iranian roommates in college who told me about their Muslim clerics teaching that women had special rays in their hair that hits the eyes of men and make them lustful. That's probably why they have signs everywhere that say things like "Sister, guard your veil". It's also interesting that the more women are veiled, the more that society that enforces the veiling seems to act in misogynistic ways. My Iranian friends told of how men make a game of groping veiled women out on the streets. So, these women are total veiled in a long black chador, and they are still getting groped. Sheesh.
It's interesting that Islam seems to blame women for men going astray. Christianity teaches it's more that you are obligated to treat everyone, even your worst enemy, as you would want to be treated. Jesus commanded this. And, you don't get to treat someone else like garbage just because they are of a different faith or not following your rules of accepted behavior.
Sometimes groups can get caught on on things without seeing the big picture. I had Apostolic Evangelical friends in high school who were trying to convert me. They didn't cut their hair, based on the teachings of their church. They had such long, lovely hair that fell below their knees. They told me that God gave them this hair so it was against His will for them to have short hair. Yet, they shaved their legs. Didn't God give them the hair on their legs so why is it ok for legs to be shaven but not hair to be cut? I don't get it.