On the excellent Himalayan Art Resources website (see link in left-hand column), there is a page devoted to ‘Religious Hats of the Himalayas’.
On sculptures, the drugpa or drukpa hat of the Kagyu order is like a crown, slightly pointed at the front. Sometimes it is made of plain metal.
16th century, Tibet, Kagyu lama, gilt copper with turquoise inlay and pigments, private collection, photo by Sotheby’s.
On other occasions the front panel is incised and/or inlaid with coral or turquoise.
15th century, Central Tibet, Kagyu Drugpa lama, gilt copper, at the San Francisco Asian Art Museum (USA).
This drugpa hat has a semi-circular shape and some side flaps that fold forward. The artist has adorned it with an incised motif and coral inlay.
On this masterpiece, the artist has adorned the front with a crescent moon and sun disc symbol.
This lama with a very expressive face also has a sun and moon symbol on the front of his hat. He holds a book in his left hand.
The drigung hat is similar but the sides are folded differently and they stick out slightly. His right hand does the blessing gesture, his left hand does the generosity gesture.