Can homeowners oc. snow plowers blow snow onto my property?

We pay homeowner's ociation fees that cover snow plowing. Yesterday we had 1 ft of snow. The snow plower came and now I have 2 1/2 feet of snow pushed onto my sidewalks and into my driveway. I was on my way to get my daughter her asthma meds, but now I can't get out of my driveway. Can the snowplower that the homeowner's ociation hired, legally put all the snow onto my property and trap me in? I can't dump my snow in other people's driveway, so why can they? I know that city plowers can basically do what they need to, but can private plowers?