Vatican II, Canon 1262, and chapel veils
Indeed it is. It states: "The faithful are to give support to the Church by responding to appeals and according to the norms issued by the conference of bishops." Hmmm. Nothing in there about chapel veils. In fact, nothing in there about liturgy. But that's not surprising: Canon 1262 is not located within Book IV of the 1983 Code of Canon Law where most norms on liturgy and sacraments are found, but rather, it is in Book V where Church property is regulated. Okay then, what about Vatican II?
Turns out, it's true that Vatican II changed nothing regarding women's headcoverings; but then, Vatican II said nothing about women's headcoverings one way or the other. In fact, to the best of my recollection, neither did Vatican I, or Trent, or Fifth Lateran, or so on back to Nicaea. Leafing through my sources, it seems that the canonical requirement that women cover their heads in church is almost completely unattested until the appearance of the 1917 Code, specifically, in Canon 1262, where we read "women, however, shall have a covered head" when assisting at liturgy. Ohhh! that Canon 1262.
I yield to no man in my admiration of the 1917 Code, but its Canon 1262 went out of force in November, 1983 (see 1983 CIC 6); the 1983 Code simply does not require women to cover their heads in church. (By the way, if 1917 CIC 1262 were still in force, we'd have to explain why we don't observe its other norms, like separate seating for men and women in church.)
Lawyer though I am, I also look through Scripture from time to time, and I recall St. Paul talking about women praying bareheaded (he does not limit it to "in church") and suggesting that it is better for them to shave themselves bald (I Cor. 11: 5 ff). What that passage might mean today, I leave to exegetes to explain. I don't see it mentioned in the Catechism, though.
Anyway, please don't misunderstand me: I'm a big fan of the textile arts, and I think chapel veils look pretty on girls and women, as do scarves and hats and those things that keep their hair in place. I'm just saying, there is no canonical requirement that women cover their heads in church today.