I find the W123 in the 240D incarnation similar to a tank in the snow. I also run 195/70-14's - Michelins - the same size as rcounts. But in snow in any car, mashing the throttle is not a common practice unless I am in a parking lot doing donuts in the snow, trying to break the rear wheels loose. The brand of tire is not the issue.

The slickness on snow comes from the tire compressing the snow or ice enough to make it momentarily become a liquid directly under the contact patch. The liquid water as an interface to the ice beneath and rubber tire above makes for a near zero friction condition. The colder it gets the less water is made, until in really cold weather, no liquid forms. At that point snow and ice are not that slick and you can maintain pretty high speed around turns and can actually effectively brake.

Jim

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Own:
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles

Owned:
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)