Believe it or not but the game actually has something of a story. Bowser and Dr. Eggman have made that by keeping the snow crystals captive it can't snow any more which results in the Winter Olympics not being able to start. It's up to the heroes to rescue the snow crystal and therewith the Olympics. One of the crystals, Frosty, managed to keep out of reach for Bowser and Eggman and gets to help Mario and Sonic in their quest. It's not much, but as a filler the story does what it's supposed to do.