Italy weather/dress in March?

I'm traveling italy in march (rome, venice, florence) and i have heard that it is still chilly and somewhat rainy around that time. I was thinking about buying a light north face or columbia jacket for the weather. Since I dont want to look too much like a tourist, and since i dont want to pack my heavy wool peacoat in my luggage, I was wondering if people in Italy actually wear brands like North Face or any other jacket of that type. I have heard that as long as its neutral color like black or brown I'll look normal. Any insight?