Sorry to hear your having no joy with your winters. I've never had Pirelli winter tires but never had a problem with Dunlop WinterSport M3 and Bridgestone Blizzak LM-32.
But I'm very surprised if your summers have better traction than the Pirelli's
One thing that does help in the snow is having slimmer tires as well as being a lot cheaper, I'm currently down from my 18" alloys to 16" steels (205/60/16).