I put a set of dedicated snow tires on my 300e sedan and it makes a world of difference on snow and ice. I bought Dunlop Graspic 185-65-15 and put them on 6" wide MBZ rims that I bought on Ebay. In snow, it's best to go one size narrower.
As far as snow tire brands, Bridgestone Blizzak and Dunlop Graspics are both great. Be aware that even snow tires are useless if the tread is less than 6/32". The two named tires have a special compound tread cap that is fantastic on ice but once it wears off it's not a snow tire anymore.
I honestly believe that snow tires are the solution to your problem.