No the tyres are rubbish in snow, the traction control is working with that what you give it and the inputs you make.The fiat 500 traction control is completely rubbish in snow, cuts power so far that it stalls the engine! Only hope is to turn tractional control off.
Had 4 different cars with TCS and they were all the same but there's 2 things to bear in mind with assistance systems. The first is the designed to work with consistent pedal pressure so if you release the throttle when you feel the wheel slip and it also reduces throttle and applies the brakes then yes it is going to stall. So point 1 either switch it off or keep your foot in and let the electronics deal with it second guessing them will stall the car.
Point 2, they can do things you can't like for example apply a single front brake. Why is that important?
Well imagine you find yourself on a single track hill with a blind corner half way up which is covered. You can't momentum run it because of the corner, even in dry conditions it's a 15mph job. But you've got your all seasons on so you're gonna give this a good go, up you go it's going well..but oh no someone else failed just after the corner and someone else failed slightly higher. You can't move out of their wheel tracks so you're going to have to take the single polished track their spinning wheel has created. You hit it all the power goes through the diff to the spinning wheel and momentum is bleeding off. At this point if you've switched TCS, you're done go home, slowly backwards down the ice covered hill. If you've got it switched on, keep your foot in, the computer will apply the brake to the spinning wheel which will act like one of those fancy E diffs and push power to the other wheel...and up you'll go.
Obviously physics are physics but learning to work with it and giving it some grip to work with tends to make them useful. Obviously if you're dead stuck...then yeah it's gonna kill power to the point of stall but otherwise better on than off.
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