I found the autos brilliant in the snow—even the rear-wheel-drive Carlton. As soon as slip occurred, it would change up just as you should in a manual. Both the Cavalier and the Volvo had "Snow" mode. Basically did everything in 4th gear. Torque converter makes starting in 4th easy and practical. Above 50 mph, "Snow" mode would drop out.
I make such a bold statement about driving auto boxes on snow and ice, yet I haven't actualy done so in person!
I base my comments on what I've read over the years stating they are not good in such conditions, and anecdotal evidence from friends. I recall the frustration my mate had in is BMW 330D Auto and his icy drive!
I suppose having done 99+% of my driving in manual, and being in control of the gear used, I would expect to be able to achieve better control. Again, no point of reference, just my perception based on personal experience.
The best technique in the world will hardly compensate for grip that does not exist. I rode an off road bike with semi scrambler / trials tyres on the road, and it was proper hairy on tarmac when slightest bit of damp around, back end would squirm around. Braking is more important than pulling away, most driver and riders who are not professionals need all the help they can get, as 99% of people just hit the brakes and close their eyes. My bike has ABS, and some people on bike forums pooh-pooh ABS, but it has saved me a couple of times when having to brake in wet / damp and encountering the 'banding' that councils make on road repairs ( some banding is bigger than others), instead of wheel locking up and going sideways it released the brakes and kept me shiny side up. Tyres are even more important on a motorbike than on a 4 wheeler.
The CBF1000 has both linked brakes and ABS, which some folk swear is a recipe for disaster!
I've yet to get the ABS to cut in, nor notice the linking affect braking control or performance. Hardly surprising given the couple of thousand fair weather miles I do.
Never ridden off road scrambler tyres on road, but I did once drive a Lada Riva with rubbish tyres on wet roads. I would expect the experience would be broadly similar!