Yea been a nightmare in the village I live in. The main road is shut so everyone has to go the back road 5 miles into town, just sheet ice and everyone is stuck down there. Iv got a 4x4 but under no illusion that it makes braking traction any better.
Couple years ago I was in my van and was going up a hill that was completely iced, soon as I stopped it would slide backwards down the hill, and touch the brakes would make it slowly spin... Rather unpleasant.
I can see why your garage might not want to touch it, it's one thing beating, filling and painting panels, but its a main structural part. I always though damage to the pillar always meant a write off. You might want to consider buying another A3, Could work out cheaper and bodywork can be hefty money sometimes.