Not sure I can add much, but a friend has a 328xi and this winter in Vermont in about 6 inches of snow it was stuck. I don't know anything about the BMW 4WD system, but the traction control system seemed to be fighting to eliminate any wheelspin and as a result the car wouldn't budge and it couldn't be rocked to move it. It was planted. My allroad drove up the same driveway as if it was asphalt.