Alienwho is wrong. The only vehicle with the guarentee of all 4 wheels turning is one will part time 4wd and locked front and rear axles.
fulltime 4wd = the front and rear axle are joined together and can turn at different speeds though to help you negotiate corners. This is useful for 4wd on roads that are only slick in spots, etc.
Part time 4wd = 4wd that is engagable when needed. There is no differential between the front an rear axles. Driving around town with it engaged on dry roads will break something.
AWD = a percentage of power is transferred and the vehicle will attempt to adjust as necessary. IE: Front wheel drive with 80% power and 20% rear, the vehicle might make that 60-40 if it detects slipping, etc. Not a "heavy duty" 4wd system.
Traction contol = not necessarily related to 4wd at all, often will just modulate the vehicle's brakes to attempt to regain traction.
As far as best on the snow, either awd or all time 4wd.