It is not so much that they won't plow the street, as they can't plow the parking area. If a stretch of road can 5 cars and one is parked in the middle when the plow comes only the first and last spot get plowed, the other two empty ones actually get new snow pushed into them. I live in an area where few people have off street parking, and fewer have enough off street parking to accommodate more than one car. If you know you will be home when the plow comes it is expected (by your neighbors) that you move it to a stretch that has been plowed, or to the end of a stretch to maximize spots that get plowed. Snow removal is also why secondary streets in Rochester have alternate parking, that is mon, wed, fri, is is on one side and tue, thur, sat, sun it is on the other. Do NOT be the douche that leaves their car on the wrong side just after a storm.
As far as getting your car hit by a plow; it happened to me, and I was SOL. The City said I couldn't prove it was them, and I had cheap insurance which wouldn't cover it unless I had someone to blame. The car drove fine, but there was a half inch wide, half inch deep two foot long dent in the door. If it wasn't a plow I don't know what it was...