Obligatory Head-Covering-For-Women-In-Church ... Thing
Is the canon law that women's heads must be covered in church still in force?
The short answer is ... NO.
The almost-short answer is ... for the Ordinary Form of the Mass (the "Novus Ordo Missae"), NOT EXPECTED; for the Extraordinary Form of the Mass (the "Traditional Latin Mass," the "Tridentine Mass," or the "Old Mass"), CUSTOMARY. Further, the original requirement did not narrow the head covering to a mantilla, nor was there a requirement regarding color. A woman's head covering could be an Easter bonnet (you know, with all the frills upon it), any sort of hat to match your outfit, or simply (believe it or not) a facial tissue held on top of your head with a bobby pin.
The longer and most definitive answer is ... at JimmyAkin.org.
In any case, men may NOT wear a head covering when in church, except for specific clerical headgear (biretta, mitre, zucchetto), and then only under specific circumstances.