[Her vision is not terribly far off in terms of Helios' chariot, then.]

Basically, yes. Ponies are horses, not all horses are ponies. Still, yes. Same basic shape.

A chariot is a wheeled vehicle that could be hitched to two horses. It generally had enough room for two people to stand inside of it, and was often used for gladatorial combat and violent races at the time and for several centuries after. But not, um, in this case. The chariot, while Helios was in it, was the sun. The horses were simply responsible for drawing it on its designated path around the world.