1) Band 2) Headpiece 1) Headpiece 
• (n.) That part of a bridle or halter which encompasses the head.
(from the article `bridle`) The reins, lines held in the hand of the rider or driver, are connected to either side of the bit so that a tug on either side turns the animal in ...
Head'stall` (-stal`) noun That part of a bridle or halter which encompasses the head. Shak. 
[n] - the band that is the part of a bridle that fits around a horse`s head
noun the band that is the part of a bridle that fits around a horse`s head