Hayagriva is a meditational deity and one of the eight-pronouncement herukas (in which case he is the wrathful form of Avalokiteshvara).
In his basic form, he has one face (peaceful or wrathful) with three eyes, two hands, a horse’s head in his hair, two legs.
He may be simply adorned with snakes. He usually has an orange moustache and beard, orange flaming hair, and a staff in his right hand (not to be confused with Achala’s sword).
The above sculpture shows him with a noose in his left hand. The horse’s head is painted with green pigment, he wears a five-leaf crown inlaid with stones and a tiger skin loin cloth knotted at the front.
In a more elaborate form, he has three heads, with three eyes and horse’s head in his hair, four to eight hands, two legs. The above holds a noose, a staff and a thunderbolt in his right hands. His main left hand holds a skull cup, the other makes a symbolical gesture or mudra and the top one holds a flaming sword. His tiger skin loin cloth is knotted at the front, the head of the tiger resting over his right thigh. He wears a garland of severed heads, snakes and stone-inlaid jewellery.
This later version shows him with his hair tied into a bunch and topped with a horse’s head, skull crowns, various pairs of legs, some victims under his feet.