From A Wiki of Ice and Fire
A hathay is a cart similar to a Westerosi oxcart, however the hathay is far more ornate. It is said that travelling afoot can taint visitors in the eyes of foreign born captains and the Volantenes alike, therefore persons of quality travel by palanquin, or in the back of a hathay.
The hathay is pulled by a dwarf elephant, it has a cushioned bench for passengers between the cart's two huge iron-rimmed wooden wheels. The slaves that drive the hathays have a wheel tattooed upon one check and are naked but for a breechclout and a pair of sandals.
The cousin of the Merchant's House innkeep owns several such hathays.
One of the known hathay routes is along the Volantene wharves.
A Dance with Dragons
After helping his passengers up onto the hathay the driver clambered onto the dwarf elephant’s back and directed it in the local tongue and by prodding it with his heel. To clear the way for his hathay the driver hooted at slaves and freemen alike.