Well, that's kind of a loaded question. If you ask 100 different people, you'll probably get 90 different responses. Each one will be right in their own way, but here's my part of it:
I didn't do so well with the factory stock tires either. Eventually, I put on Cooper Discoverer ATR tires in the stock sizes. I had been using the same type on my Jeep for snow plowing and loved the way they bite into the snow, so when the time came, they went on my dually and also my wife's Durango. Best tire on snow we've had. They have a fairly aggressive tread, while not being over the top so that they make a good all around tire, even when it's not snowing.
The idea behind skinny tires is that for snow you want the most weight possible in the least amount of space as possible. This concentrates the weight to push down through the snow and bite on pavement, rather than floating on top. A big, fat tire will disperse the weight over a larger area, thus making the tire "float" on top of the snow. This is why duallys are so bad in the snow. The two rear tires on either side disperse the truck's weight, rather than concentrating it. Perfect for towing and hauling, not so much for snow driving.
I'm not sure that radically changing your tire size is necessary. Just a good set of tires with some nice tread. My Jeep is much better in the snow than my dually, but with these tires, I can make due with the truck.