I was inspired to give Demeter Erinys/Demeter Melaina snaky hair after I learned that Demeter’s Archaic wooden statue in her cave at Phigaleia looked quite unusual. Pausanias was given a description of it (it had been destroyed long before he visited Phigaleia): "It was seated on a rock, like to a woman in all respects save the head. She had the head and hair of a horse, and there grew out of her head images of serpents and other beasts. Her tunic reached right to her feet; on one of her hands was a dolphin, on the other a dove" (Pausanias, Description of Greece 8.42.4).
Jennifer Larson means that this Demeter is a Mistress of Animals and has close affinities with the gorgon Medusa, who similarly sported snaky hair, mated with Poseidon, and gave birth to a miraculous horse (Pegasos). This part of the story, a miraculous horse sired by Poseidon upon a goddess closely concerned with fertility, seems to be very old and was originally probably not a part of the story of Demeter’s search for her daughter. Arion’s conception and birth was also told in the lost epic Thebais, usually dated to the seventh or sixth century BCE. There the goddess is only called Erinys, which was also the name of an old Mycenaean goddess (e-ri-nu in Linear B). Jennifer Larson suggests: "The Arkadian cults of Demeter resulted from a complex process combining the old Mycenaean goddess Erinys, who was early on linked to Poseidon Hippios and whose offspring was a horse, with the Panhellenic and Eleusinian Demeter who bore a daughter" (Ancient Greek Cults: A Guide by Jennifer Larson).
Now we know what depression looks like on a god...on Demeter anyway