This video has a very good walkthrough by the creator. At the beginning of the course, turn around and drive across the bridge. Turn back around and drive toward the snow, but do not touch any part of the track between the bridge and the finish line. Instead, veer off to the right after you reach the end of the bridge and drive off the course into the snow until you reach the finish line. At this point, drive further off the course until Lakitu picks you up and sets you back.
Mario Kart 64 Shortcut Video Walkthrough Series for Nintendo 64
Mario Kart 64 - Frappe Snowland Shortcut Video
