Where does "it" say that a woman's hair is her "head covering"?  I don't know.  I've not read this.

 :surprised:
How disconcerting to re-visit this topic as a debate among traditional Catholics!  First time was in the early 1980s with rapidly modernizing Mennonites.  The first outwardly distinctive item to go was the woman's head covering.  These Mennonites will be in church tomorrow in clothing indistinguishable from the Baptists and Methodists on the same street. (To their credit, they will all be dressed better than the Catholics at the novus ordo!)  It is how the devil works to attack the woman first.  Satan spoke to Eve, not to Adam.  Keeping in mind the Mennonites actually lost the Reason for the woman's head covering when they rejected belief in Our Lord's Real Presence in the Blessed Sacrament and in t the Tabernacle, back in the 1520s, it is a tribute to the power of what became only a custom, that it lasted close to 500 years because it it is based on Truth, Catholic Truth.  To read the comments of Catholics who supposedly have the Truth speaking as Mennonites who do not, is frankly, distressing!   The error comes from the poorly worded King James English Bible.  The implication is that the hair IS the required covering.  Check the Latin or Greek and it becomes clear.  Neither St. Jerome nor St. Paul taught such a thing.  Among Mennonites, if one goes back to the 1930s, most were using German Bibles, which, still incorrect, did not give this impression.  The last of the Mennonites to rely exclusively on the German died out in the 1980s.  This goes to prove that when the doctrine strays, practice eventually follows.  I've wondered for some time why God allowed me to "waste" so much of my life in error.  But it is coming clear as I see Traditional Catholics follow the same path to perdition.  
If anyone had told the mainstays of the Mennonite church in the 1980s that by 2013, earlier, actually, they would be dressing in jeans, watching TV, having electric  guitars and drums in their church "services," and that not a single woman would wear a "covering," that there would not be any cape-dresses or straight coats among them, it would not have been believed.  There were a very few voices of warning, all of whom were scorned and rejected as doomsayers.  Most of these are no longer living.  But look what happened!  Those who say the sspx can't/won't fall, and that "nothing has changed," take a lesson from history!  
By the way, ladies and girls, our hair is not the covering.  Wear a veil when in Christ's Presence!
Even the old Mennonites used to joke that if God made hair for a covering, only bald men dare pray in church!  Better get out your razors, fellows!  Prerequisite for ordination, you must be bald!