Artemis' Chariot, also known as the Moon Chariot, is made of silver and pulled by four golden reindeer with silver horns. The reins of her chariot are made of silver too.
Selene's Battle with Typhon
Before Artemis became goddess of the moon, the Titaness Selene owned the moon chariot, which she drove across the sky at night. When Typhon began his path of destruction to Mount Olympus, Selene rode into battle with the moon chariot. The encounter left the scars and craters seen on the moon up to this very day.
Artemis summons her chariot after the battle against Atlas to get Percy Jackson, Thalia Grace, Zoë Nightshade, Grover Underwood, and Annabeth Chase to a safe place, where she then turns Zoë into the constellation, "The Huntress". Artemis then leaves to attend the winter solstice meeting at Olympus.
Percy mentions that Artemis is fighting Typhon in her chariot, a monster who broke free a second time, and came to help Kronos. It is stated that it looks like Santa Claus' sleigh, except for the fact a girl is driving, and there are silver arrows being shot out of it.
Artemis was the moon goddess because when riding in her chariot the people of Greece thought she was driving the moon across the sky as her brother, Apollo, drove the sun across the sky.