With a decent set of winter tires, I don't think you'll be worse off than any other RWD car.
It's not going to be nearly as good as your 328 XI for snow though.
The real downside of the M3 for everyday usage is the gas mileage. But if that's affordable, I would definitely go for it.
2011 BMW 335i E92 - Le Mans Blue, 6MT, M Sport. JRZ RS Pro, Quaife LSD, BMW Perf Exhaust