Mythology – Horse / Ass

General – Horse : royalty, divinity, otherworldly transport, water and storms, especially thunder,
peace and good harvest, indestructibility, purity and loyalty (one of Buddist's seven treasures)

Ass : matter, body, misfortune, rampant sexual desire, ridicule, lazy, stupid, poverty

Culturally Specific – royalty: Celtic kings and priests's chariots drawn by white horses, Irish kingship rite's symbolic copulation with a white mare, then bathing in her broth, divinity: Welsh Rhiannon, Celtic Epona, Old Grey Mare (aspect of the Celtic goddess in winter at Yule and New Year)

Examples of specific myths – unicorns, Pegasus, centaurs, hippogriffs, nightmares, Slepnir

Otherworldly transport:

White horse of Lugh (Celtic)

white horse of Mannanan (rides across the top of the waves, rider becomes invulnerable) (Celtic) , Slepnir (Odin's eight legged horse) (Norse)

Horses of fire pulling Elijah's chariot to heaven (Hebrew)

Pegasus who ascended to the Heavens (Greek)

Storms :

Seahorses (with backward facing hooves) pulling Poseidon’s chariot (Greek)

Pegasus born of the union of Poseidon with a Gorgon and carried Zeus's thunderbolts (Greek)

Here's a great site for Horse mythology

Peace and good harvest: Shinto gods and ritual horse racing, Celtic harvest festival of Lammas

Modern view of – Seventh animal of the Chinese Zodiac whose sign denotes money smarts and cheerful but quick to anger, Yang symbol of good luck along with horseshoes (European myths agree)

Famous horses – Silver (Lone Ranger), Scout (Tonto), Trigger (Roy Rodgers), Hans (the counting horse), Mr. Ed (The talking horse), Frances (the talking mule), Black Beauty, Misty of Ciquotague, Shadowfax (The Lord of the Rings)