Since nobody else has answered I will make a suggestion: Find a hotel with a large car park, and just park there. This often works in the the Dolomites (also Italy). If you want to be nice, you can ask permission, but you may get a "No!" or at least be asked to pay. In the Dolomites there often are very large car parks in the famous passes (such as the Passo di Sella, Passo Falzarego or Passo di Rolle) which are free or at least cheap. I have never been to Cervinia, but I suppose it cannot be too different there.

http://www.summitpost.org/phpBB2/viewtopic.php?t=52628
here the same topic with the answer