In regards to snow, both cars will be iffy in the snow if you stay on summer tires - AWD does nothing if you can't get any traction. With what we get you'll fine in the M3 with snows on.
I live in NJ as well and went through the same dilemma as you. The car I bought had to be able to be daily driven unless the weather was extremely terrible.
I do think at first glance the Audi has a better looking interior, but after some extended seat time boy is it a handful. So many buttons, everywhere - it really becomes distracting when you need to use one of the buttons. In addition you still have an iDrive type system to manage as well.
The M3 is the everyday car for the guy who enjoys driving. A quote that stands out in many reviews is that the M3 is not really top of class in any one category, but it is consistently at about a 7 in all - very few cars can claim that.