In our road association, the last person in has an agreement with the plow contractor that they can turn around in their driveway, on the condition that they back in a couple of truck lengths - just far enough to get off of the upgrade at the end of it - and then drop their plow when they pull out.  Every so often the contractor hires a new guy who doesn't know, and who tries to back in and pull out with the plow up.  The result is that after a couple of passes, the upgrade gets so packed with snow that even the plow truck has trouble getting out!  So the resident has to keep an ear out for the truck, and try to run out and tell him what the agreement is, and why.

I don't think you'll have much luck demanding that the plow contractor replace material that was plowed off, but you might want to request that they not plow if the ground isn't frozen (especially if it's only a few inches and will melt soon), or that they raise their plow slightly if the ground isn't frozen.