If D3 is the same as D2 they are all open diffs without mechanical locks even if is torsen/limited slip and only 'locking' is that control unit slightly applies brakes to the spinning wheel in pulses. If 1 wheel loses grip completely or has very little grip you are moving nowhere, this is where old school quattros with manual rear and centre diff locks were much better, also having winter tyres helps a lot, most of the time FWD car with winter tyres will do better than quattro with summer tyres in the snow. I have even seen old Audi 80 with both diff locks engaged spinning 3 wheels and not going anywhere with summer tyres but there was not much problem for me right next to it with a front wheel drive Citroen XM with winter tyres I had at the time.
If you did not have drive to front wheels it would be the same as having no grip and you would not be driving at all. I actually had one of my friends quattros brake front driveshaft outer CV joint and it stopped moving, just spinning the broken drive shaft. They did actually disconnect the shaft from outer CV joint, secured to the body using rope at an angle so that it could not turn and were able to gently drive home. The reason your rear wheels spin is because the car is lighter in the rear so have less grip. Always keep you tank full and a couple of bodies in the boot in winter to have more weight and more balanced grip in snow
