Running snows until "worn out" is foolish.
I run worn snows down to the wear bars in the summer. Might as well use em up.
Snow tires help you stop, turn, and go. AWD/4WD help you go. Having lived *in* the CO mountains for the last 3 winters (and having the driveway voted "worst" by the guys who plow most of the county), with a front wheel drive car and four non studded snow tires... I can tell you that its the tires that matter,
4WD helps you steer and brake as well.
Static friction is greater than kinetic friction. That means you have more traction when the tire isn't slipping, and once slipped, it's harder to regain. 4WD keeps at least 1 wheel in the front and one wheel in the back turning. If the excess torque (above slippage torque) is minimized by feathering braking or the gas pedal, the skid can be managed/avoided. With good feathering all 4 wheels keep contact by not driving the differential into differentiating.
Example:
2WD brake in a straight line, apply brake, all 4 wheels skid. Driven wheels slow down and non-driven wheels lock up. When you get off the brake the non driven wheels may still skid as there is insufficient traction to spin the wheels back up to vehicle speed.
4WD: brake in a straight line, apply brake, all 4 wheels skid, however they are still spinning just below vehicle speed. The direct connection to the engine keeps the wheels rotating, they all can't lock up unless you jam the brakes so hard you stall the engine. (Stick shift) If you get off the brake you can re-establish tire/snow contact and regain control. An automatic compromises this effect as you don't have a direct hard connection from the wheels to the engine..
In turns, even though the front wheels may slip, driven front wheels will still pull you into the turn if you feather the gas. In 4wd the rears provide added boost to keep the vehicle moving.
Note that I'm talking snow, not black ice. Real glazed ice on the road generally means you're going for Mr Toad's wild ride. (yeah, yeah, Blizzaks) Worse yet is wet ice - no control.
With the advent of ABS braking control has been taken away from the driver in a skid. This is undesirable as when one wheel slips, ABS kicks in even if the other 3 have good traction still. ABS usually increases your stopping distance at the expense of mandated pulsed braking to salvage steering for a panicked driver.
So in snow,
Stick > automatic
4WD > AWD
AWD > FWD
FWD > RWD
No ABS > ABS (for a skilled driver)
Snow tires > All season tires
Fresh tread > worn tread
Subtle changes > Texas stomp
This leaves a zillion combinations where arguments can be had over which is better. That said, I'll take my 4WD snow tire shod, stick shift, high clearance truck over almost anything else in snow. I've been in snow deep enough to roll waves of snow over the hood.
For inexperience snow drivers, go out and practice. Turn big slow donuts in a parking lot in the snow, building speed until you feel the wheels start to slip. Play with holding that speed and managing the speed and turn at the slip threshold. Try some skidded turns and regain steering control by widening the turn and easing off the gas. Get up to 25mph and then experiment with braking, applying brakes slowly increasing brake pressure until you feel the wheels slip. Ease off just a little until you feel the wheels re-engage. Find the maximum stopping force you can apply. Learn to feather, ie small adjustments constantly adjusting to suit the response. When going up a hill in a snowstorm, try goosing the gas until the tires slip and then ease off. That's your maximum torque available to get up the hill, and you might need it at the steepest part. Momentum is your friend up hills and your enemy down hills.
Small losses of traction is information. Massive loss of traction and massive corrections lead to loss of control. Leave huge space between you and the next car.