From Wikipedia:
The story is different in single- and multi-player modes, but the gameplay remains identical.
In single player, the story centers around the snow goddess Sayuki's love for a boy who lives in a nearby village. Upon visiting the village one day, she learns that the boy has fallen under a curse, sleeping permanently. Sayuki then travels across the land with her pet snow rabbit, Toto, to find the ingredients for the cure to his curse.
In multiplayer, the story is about a beauty contest held by the Snow Goddess Tribe. Sayuki and her younger sister, Koyuki, decide to compete for first place. The contest is a trial race for the two sisters to destroy the most ghosts and collect the most snowballs in their path.