Cowl

A cowl is little more than a hood.  It was put on over the head much like a shirt, as the only opening was the one where the face looked out.  It didn't end at the neck, however- merely gathered there and then spread out over the shoulders in a shoulder cape, as in the picture.  The cowl was normally worn with a cloak or cape.  It was the predecessor to the chaperon.

For more information:

Costuming 101