It sounds to me that they're talking about the snow being pushed by thw plow down the street, with their house being at the end of the street, then pushing the snow off of the road onto the yard. The place where snow is left by a plow sounds like something that happens at the discretion of the plow operator, making it the very type of decision to which governmental immunity does apply. But whether we call it "dumping" or something else, do you have any case law or other legal authority? Because, as you know, "That's not fair" doesn't carry the day in court. I hope you don't act like jk and, unable to back up your words, attempt to reverse the burden of proof. This is you guys' assertion.
The sovereign immunity to a private contractor angle, on the other hand, is interesting. Clearly there are contexts where government immunity carries over to private contractors (even though, in my opinion, that rarely if ever should happen).

