Paul, your car has ESP which includes stability software, throttle traction control and electronic differential lock.
The juddering under wheelspin below 30mph is the classic sound of EDL working, by applying a braking force to one (spinning) wheel, torque can be transferred to the other side of the axle in an attempt to overcome the non mechanically locking diffs tendancy to put torque to the least resistive wheel. AFAIK on the S3, the throttle is usually cut first when wheelspin is encountered (the traction control) but perhaps in the snow, the EDL comes in as a second line effect.
EDL used to be standard fare on the a3 1.8Ts before ESP/ASR etc was introduced and to be honest, it made a alot of noise, but gave no more forward motion /ubbthreads/images/graemlins/smile.gif