You need better winter tires. The Sottozero are known to be more dry road focused (like the Michelin PA3) and do not do well in deep snow. There are closer to an all season that a true snow/ice tire. Get a set of Blizzaks, Nokian, or x-ice and you will get much better results. Not as good as AWD for sure but very liveable in my experience.
2012 C63 coupe | Obsidian Black | Performance Package (481hp, 443ft/lbs)
1996 E36 M3 coupe | Estoril blue | Dedicated track car... heavily modded
2011 M3 coupe | Jerez Black | ZCP/DCT | Sold but never forgotten nor will the love affair end
2010 M3 coupe | Alpine White | 6MT | Sold