Zebras occupy eastern part of the Old World because of savannah on the Cutiemap at the west from Equestria and, well “Fallout: Equestria” where they are used as China. They are rather unstable feudal empire where small tribes live by the old ways under protection of mighty kings who have actual armies.
Chariots are piloted by nobles who are not able to fight as cataphachts or feathered ones but can still obtain a wagon and a couple of servants. They use spears or javelins, usually chasing the already broken enemy or trying to reach for the archers.