Some drivers try getting off any icy patch on a street by gunning the accelerator to have the spinning tires melt through the ice to a patch of bare pavement. The spinning wheel, incidentally, actually spins at double the speed shown on your speedometer, which is fast enough to cause a tire to fly apart.
The bigger problem is that as soon as tires hit terra firma, the transmission is stressed as the torque of the engine is applied to all components of the drive train. Soon enough, the weakest link will fail. Often it's the universal joints or CV joints in a front wheel drive car, were designed to handle. But any part may turn out to be the weakest link, and give you a hefty repair bill.
To protect your tires, your drive train components and your transmission, take it easy when you try to "rock" your car out of a snow bank, or get it to accelerate on an icy patch of road.