Snow tires matter much more than it being 2wd. AWD and 4WD are worthless in the ice just like 2wd.
Personally living, and have lived, in snowy area while I prize winter tire on snow I also prize 4WD/AWD, without them in many cases I'll have had to beg for a tow, no matter how good winter tire I can ever mount.
In some condition, like little snow, you only have slippery roads due to the moisture of salt/snow/dirt on the road and 4wheel help reaming on trajectory but you may still drive on 2WD at least if you are a good enough driver, on heavier snow 4wheels means have enough traction to advance and enough grip to still have traction when some wheel slip.
I grew up living on the side of a mountain in Montana. 1000 foot climb from the highway to home. Could not make it home in winter with snow tires and 2WD, period. You'd end up fish tailing and generally turning a snow packed road into a gleaming sheet of ice. Which, makes it worse for those with 4WD as now the snow pack is a polished sheet of ice.
4WD helped, but was also not always sufficient. I've had a 4WD SUV slide directly sideways after coming to a compmete stop on an incline. Some of the grades were up to 14%, not highway quality, but private road.
Only relatively assured way to get home was 4WD, snow tires and chains. And you could skip the snow tires if you had the chains.