Not quite.
Even as recently as the 60’s, just before Vatican II, it was customary for women and young girls to go to Mass with their heads covered.
In fact it was very common for a young man to give his girlfriend a fancy mantilla on her birthday or as a Christmas present.
Turned catholic in late 1950’s. All women that went into church had heads covered. Some with scarfs, but most had hats. If one wanted to stop in church to pray, many kept a clean hanky for the head covering...a sign of respect..