I... won with all the cars. However I'd advise you to use Enforcer, Redneck, Monster or Banana. These are easy to use and you'll definitely win with one of them. Also, if you don't get first place in the FIRST race, don't restart the race and lose a tire! Restart the whole event, you'll still be there. Although you need to use the tires at the next races.
Just keep trying and you'll do it right, I'm sure!