Unfortunately, the advice on skidding is only half-right. The basic physics here are that the rear of the car is moving forward faster than the front of the car, and picked a direction (left or right) to move to get around the front of the car which is blocking its way.
So:
1. Steering into the skid is always correct (provided you can safely move that direction), because it puts the front of the car in front of where the back is trying to go, which slows down the back.
2. Never hit the brakes in a skid if you can at all help it. (I've had to once because I went round a curve and discovered that the highway had gone from moving about 75km/h to stopped with no time to slow down, luckily I didn't hit anybody when I ended up in the next lane over)
3. In a RWD car, decelerating will help, because it will slow down the rear of the car, allowing the front to move forward faster relative to the back (think of the effect of attaching a string with a weight to the back of a toy car).
4. In a FWD car, accelerating slightly will help, because it will pull the front forward faster. Again, if you want the model car version of this, it's like pulling on the front end of the car with a string. Skids are also a lot less likely because the FWD is pulling the front forward rather than pushing the back forward. Of course, decelerate again as soon as you're on more solid surface.
5. In a 4WD car, my understanding is that skids are both unusual and pretty easy to correct, but I think there are techniques involving switching into FWD mode or only braking the back wheels.
But you'd be very surprised how many people live in snowy parts of the country and also don't know anything about handling skids. They're usually pretty easy to spot, since they're driving about 15 km/h when road conditions warrant closer to 50 km/h. My general view on driving in winter conditions is that the flakes I'm worried about aren't the ones falling from the sky, but the ones behind the wheels of other vehicles!