This is an old trick that most drivers know after driving much on icy roads; carry a small bottle of bleach, a sponge and plastic gloves in the trunk. Also, carry a bag of cat litter.
I honestly believe some cars have a mind of their own; they love to see you spin their wheels on ice; sort of getting back at you for not warming them up before you backed out of the driveway.
Spinning the wheels only makes it worse, so slip on your plastic gloves, pour a little bleach on the sponge and wipe what you can reach of the face of the tire. The bleach makes the tire bite into the ice, and away you go. If you're stuck in snow, the cat litter sprinkled in front of the tire might get you out of there.