In reply to chrisps:
In the summer it is reasonably easy to find free parking (you might have to walk for ten minutes to the lift, assuming you are taking it). When I go to Madonna I usually keep driving just beyond the main town towards the pass. Here there is a big layby parking area (overlooking the baby ski slopes) that always seems to have space (even in winter, for ski touring).
It would make more logistical sense to park at the bottom of the Brenta range, for example Tione, and then take a bus up to Madonna, and walk back down to the car, but that might be difficult to coordinate with flights and so on.
You could completely eliminate the car. For example:
Catch a train to Trento (trains very cheap here) and then take the coach from the bus station beside the train station to Madonna. When you finish your VF, head down towards the east (Molveno/Andalo). From there you can eaither walk or take a cablecar up the Paganella and then descend the other side towards Terlago. From there either a bus or panoramic footpath back to Trento. There is a refuge on the Paganella and plenty of old WWI bunkers between Terlago and Trento for an overnight doss (if I am around you could sleep in our luxury one).
If you were stuck overnight in Trento waiting for the coach here is a good hostel place very close to the train station.