As Ace says, the Type R is not really any different from any other Scooby in the snow, if anything the DCCD will improve matters as you can lock the centre diff for increased grip when it's really slippy.
All wheel drive obviously helps in the snow compared to both front or rear wheel drive, but only when driving, under braking AWD makes no difference.
The real secret to a car being good or bad in the snow is the tyres! Wide, low profile summer tyres are designed to work when its warm and when you can heat up the tread enough for them to function; in the snow, they will be effectively frozen and offer very little grip.
A thinner tyre width has a smaller contact patch, which means the weight of the vehicle is applied to a smaller area which helps the tyres sink in and cut through the snow to grip the tarmac below.
A larger profile allows for more side-wall movement which helps generate heat in the tyres which inturn provides more grip.
A winter tyre has a high silicone compound which is designed to work better at lower temperatures, so the rubber doesn't freeze on colder days which helps with traction and braking not only in snow, but also in the wet, on ice, or even on dry tarmac when the temperatures are below 14 degrees.
The tread pattern on winter tyres is designed to disperse standing water better and also helps to cut through snow. Small slits in the main tread block increase grip on Ice.
From my experience, don't worry so much about weather a car is good in snow or not, worry about whether you have the right tyres fitted for the conditions! Fit winter tyres from November to March and you'll never go back to driving winters on summer tyres!