You Don't Need a Fat Bike
Winter bike from Thomas Rinfret on Vimeo.
I'm not saying that you shouldn't get a fat bike, but a mountain bike works fine on packed snow. Just layer up and maintain (clean and lube, especially if you ride on salted roads or sidewalks) your bike! But, I'm tempted by those 3"+ tires too.
More Info:
Wikipedia - Cold Weather Biking