Thanks for all the insight. Believe it or not, we actually had a shovel and some other snow gear in the car that night, and it just didn't help. The plows in Minneapolis just didn't clear the alleys enough to make them passable after that storm.
We had the vehicle checked out the other day and it didn't appear that we did any damage. The smell persists, although it has faded quite a bit. It's hard to find a time and place to air it out during a Minnesota winter.
I was thinking about spraying down the interior with Febreze. Has anyone tried that, and had any success in killing a burnt rubber smell? Somehow I don't think the little pine tree deodorizer is going to do the trick this time.