1) As seen in the video, though normal tires won't be quite so flexible as the tires shown, tires flex QUITE a bit when you rev your car to a start. With a common knowledge of the fact that materials get harder in the cold, severe cold weather could pretty pheasably cause damage to the integrity of the material should you rev them too fast.

2) The cold air not only makes the rubber more dense, but it makes the air inside the tires more dense as well. That means your tire pressure--should you be the more common not-so-diligent-pressure-inspector--is lower than it should be. This in and of itself causes the amount of surface area of the tire touching the ground to decrease, which will give you less traction to begin with. Traction is good during the winter

3) By scrambling your tires as fast as they can go, you're causing QUITE a lot of friction, and even cave-men figured out the unavoidable side effect of such is heat. This heat often leads to the snow under the tire getting melted, meaning now you're trying to skid on a water-slush-ice-snow combo. Trust me, snow tires are made for SNOW, you're better off dealing with just that.

4) It wastes gas! Seems a little obvious that gas is wasted when you're sitting there pedal to the floor but not moving, but whats more you're making your car work pretty hard to go nowhere. It's a bigger waste than you'd probably think, and not so nice for the environment either!