Finnish guy here, I know something about the topic :-)
Yes. You do need winter tyres on a 4WD. As someone said above, it's not only the traction. It's braking and turning you need to worry about.
Ordinary tyres are useless on snow. Snow fills the texture which is designed to channel water rather than snow. Ordinary tyres perform as good as slick racing tyres on snow, that is: not very well.
Swiss insurance companies require using winter tyres. Most alpine roads require either winter tyres or snow chains when it's snowing (the blue sign with a chained tyre on it).
When choosing winter tyres, I'd recommend sticking with the 'premium' brands: Michelin Alpin, Bridgestone Blizzak, Dunlop Wintersport, Contintental, Goodyear and Nokian (of course).
Compared to summer tyres, an ideal winter tyre is more narrow, thicker and of slower speed rating. For instance, if the summer tyre is 245/40/18V, the winter tyre could be 205/55/17H.
If you drive to the alps, keep a pair of snow chains in the boot. Even when your car is equipped with winter tyres.