At 13 years and 160k miles your car is right smack in the phase for needing a thorough suspension inspection, if not overhaul. Pay particular attention to the links and bushings in the rear suspension. They can give all sorts of unintentional steering movements under load. Mercedes uses a lot of rubber in its suspension designs, which makes for a great ride when new, but can lead to a lot of slop when they get old and dry.

Also, buy good rain tires. Some are definitely better in the wet than others.

FWIW, my 300E performs well in the rain. I've had it at highway speeds in absolute downpours, and it handles pretty well, and it's an early (lighter) model.