Arborvitae do have the ability to regrow in areas where they have been damaged to a point. If the branches have been totally girdled, any growth would come from below that point. You will have to wait and see what comes back before pruning away what is actually dead. It may take several seasons to recover. I would expect that you will have to protect your screen every winter from now on, especially in the years when there is heavy snow fall.
