hood

…main head covering was the hood with an attached shoulder cape and a long extended point, or tail, known as a liripipe. By the 1420s a new way of wearing this hood was tried. The face portion was placed on the head, then the cape was arranged in folds like…

…heavy cloth or fur-lined; this hood, tied loosely under the chin, is seen in many portraits of the time. Sometimes the steeple hat was worn on top of the hood.