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.
2016 M2 | Long Beach Blue | 6MT - current
2015 M4 | Austin Yellow | DCT
2014 Corvette Stingray | Z51 | Torch Red | 7MT
2012 MB C63 Coupe | Performance package | Obsidian Black
2011 E92 M3 | Jerez Black | Fox Red | DCT | Competition Package