That is the scary thing - I have snow tires!!!! Nokian Hakkapelitta NRWs to be exact, nearly new. They have tons of ice gripping sipes, yet I still slid immediately - not much you can do on pure, smooth ice...
My mom was following about 10 minutes behind me, so I called her immediately after this happened (she hadn't left yet). She went to the same stop sign, in her Acura MDX with giant knobbie tires, and she still slid even after she knew how slippery it was from me calling her (not as far as I did, though). It was damn slippery...