Whether or not such exposure would be deemed inappropriate has little to do with which gender is dominant. While there is any number of people of both sexes who would gladly walk down the street naked just because they could, even the most staunch patriarchist would generally cover up in public. Why?
Because primary and secondary sex characteristics of humanity are considered "posessions" sophisticated cultures (read: not tribal). Something that shouldn't be shared with others because those characteristics (breasts & genitalia, etc.) are not other's for the taking.
What are the characteristics of a society that might admonish "covering up?"
Posession (what's mine is mine)
Whether or not intercourse itself is viewed as a status symbol in the socity (e.g., ancient Greek or Roman sensibilities).
As for whether or not a patient would be covered up depends on convenience. On the battlefield, the first priority is to save the life, not protect dignity. Whether or not something is covered is only a matter of convenience, nothing else. (Likewise, nothing would be removed that wasn't necessary because time is more important than anything else.)
However, the further you get from crisis, the more social mores kick in. Even on an operating table, if the environment is controlled and prepared for, only that area of the body being worked on is exposed. Why? For one, because cleaning up offal is much simpler when a drop-cloth is involved. For another, when people have time to think about social mores, they tend to act upon them.
Therefore, the issue has nothing to do with matriarchy or whether or not it's a warrior society. It has everything to do with the social mores of your society.
Curiously, our own society is changing from a very sexually closed society to a very sexually open society. The reasons range from greater acceptance of LGBT individuals to an open Internet that permits sexting from a very young age. Which means both politics and communication technology impact social mores.