We haven't had snow here yet, but the winter before last we had our 1 days worth.
It just happened to coincide with my daughters inset day at school, so we went sledging on Butser Hill.
I took my RR Classic 3.9 Auto (pre ABS) with Michelin M+Ss.
It had rained, frozen and then snowed. There was about 2" snow on the road, with sheet ice under it.
We had to stop on a steepish bit as someone was trying to park.
Pulling away was difficult but would have been much harder with a manual.
Being a a lazy git, I tried to get as far up the hill as possible. The single lane track at the top has gert great lumps of wood along the side to stop people driving on the grass. There was a 2-3' deep drift across the track at the gate into the top car park, which even I would not attempt, so I had to reverse 200 yards back to a turning point. As there is less than zero engine braking in reverse with an auto, I had to lock the thing into 1 and let it roll.
There were horrible noises from the transmission and drive train but we got back down in full control.
So, in my experiance auto is great for going up hill, and crap for going down in reverse.