Well actually... 4x4 is worse for going downhill on ice. If one axle loses traction (which would be much more likely on summer tyres), the other can initiate a slide.
This is the exact reason people dont like 4x4 on ice. AWD (usually) lessens the problem - which is why i said they absolutely help with the correct tyres.
And again - DONT SLOW DOWN when going down hill. Your brakes WILL lock a wheel and you WILL slide. Slow down BEFORE you go downhill. If you havent experienced this truth, then you havent driven downhill on ice (which is preferable).