Any type of snow covered routes in hilly areas, just go for dedicated winter tires. Either swap them in the OEM rims, and keep the A/S For the warmer months (although change out the OEM’s when you get the chance), or get dedicated set of winter wheel/tires, maybe in 18” or 20”, where you get much better options for tires.
The all terrain / all weathers may do better in deeper snow due to the larger blocks, but they are no better and often times worse in ice conditions due to hard compounds and less edges.
True winter tires on these cars make them absolute tanks in the severe conditions. It’s worth it if you are doing any driving outside of suburbia/urban shopping/commuting.