Another vote for dedicated snow tires here. I owned a 1994 E420 with ASR for 6 years and I put a set of Hakka RSi snow tires on it in the winter. It was awesome! Drive that 300 in the snow. It might rust fast (I keep my 97 E300D out if the salt), but you shouldn't get stuck.

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NOW: 2017 C43 AMG, 2006 Wrangler Unlimited Rubicon, 1966 230SL, 1980 450SL (for sale!)
PAST: 2006 C230, 1997 E300D, 1994 E420, 1994 Neon Spt Cpe, 1984 300ZX, 1983 Celica GT, 1976 Electra Limited, 1984 Honda Nighthawk 650, 1979 Suzuki PE175, 1978 Suzuki DS100
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