The Z71 tires are as bad as the 20" Goodyear Eagles. GM has crappy choices when it comes to OEM tires on their vehicles.I had the stock 20's on my Silverado and form what I could see they wouldn't be great in the snow though I didn't have them long enough to try them out. IMO they weren't great (though not horrible) in plain wet conditions. It does look as if the Z71 tires (though not 20's) would provide better traction.
I ended up going a tad aggressive!
Good luck.