By coincidence I found a nice picture on the page of
Saint Francis Veil Company, Veneta, Oregon, USA
showing the Vergin Mary covering her head with a veil.
You will find detailed information here.
Caravaggio: Annunciation of the Birth of Jesus, 1608/09
Musée des Beaux-Arts, Nancy, France
Mary with veil
In church:
© pictures: Orbis Catholicus
In presence of the Pope:
Jacqueline Kennedy and John XIII
Queen Elisabeth II in the Vatican
The Spanish Mantilla is a veil fixed over a high comb (peineta):
© picture: Orbis Catholicus
A free download of Paul K. William's book here.
More information and pictures: