Chronologically, Ventus’s adventure takes place after Terra’s in Kingdom Hearts: Birth By Sleep. He is not allowed to take part in the Keyblade Master exam, and not present when Master Eraqus tells Terra and Aqua of the Unversed threat and Master Xehanort’s disappearance. I’ll try to be vague and keep spoilers to a minimum from here on out.
That doesn’t mean Ven was alone. While Terra and Aqua were talking with Master Eraqus, Ven found himself confronted and taunted by Master Xehanort’s apprentice, Vanitus, who makes Ven worry about Terra’s safety and want to search for more answers from Vanitus and Xehanort. This inspires him to follow Terra. Of course he’ll also take care of any Unversed he finds along the way. He takes off from the Land of Departure on his keyblade turned space-traveling surfboard and heads to his first destination, the Dwarf Woodlands.
Once Ven arrives in a hilly, somewhat mountainous area, he starts hearing some whistling. He looks down onto the path below him and sees the seven dwarves, happily whistling as they head off to work in the mines. The discovery delights him, and he follows them along. Let me just say, that his reaction is absolutely adorable, and he reacts with similar happiness and delight to a number of the Disney characters. Ven heads down to follow the dwarves, fighting Unversed on the way.
He then goes down to introduce himself, but the dwarves mistake Ven for a bad guy and all run away and hide. Except for Dopey, who runs into a wall and drops. Ven tries to explains himself, and ask about Terra, but the dwarves still don’t trust him and think he’s a thief. Ventus then has to them out by fighting and saving them from the Unversed in the mines.
Ven leaves the mines and finds the dwarves’ home, a cottage in the woods. He hears a woman’s scream, and runs to investigate. He finds Snow White, cowering and crying in a dark forest. He tells her everything is okay, and offers to help. He then has to help protect her from Unversed and living tree monsters. (This was probably one of the most annoying parts of Ven’s story.) He escorts her back home. He steps out for a bit, then the dwarves come back home. When Ven returns to the cabin, the dwarves are still angry, even after Snow White explains how Ven helped her. It turns out Snow White is in danger since she’s a Princess of Heart, they still don’t trust Ven and think he’s there to cause trouble.
Ven leaves the cottage, and runs into and defeats an evil tree Unversed boss while hoping to find and catch up to Terra. He finds an old witch, with apples, instead. He asks her about Terra. She gives some cryptic response and leaves. Ven then leaves the Dwarf Woodland.
