Enjoy your own private Iditarod, or at least get a taste of what it's like to be a dogsled driver. Several companies offer one-hour, half-day, full-day and even overnight trips. You might even be offered a chance to drive the team yourself. Did I hear someone say "mush"?
The International Pedigree Stage Stop Sled Dog Race is a dog sled race from Jackson to Park City. Their website has info for registration and all race events.