Moisture not only comes from the snow, it also comes from the body in the form of sweat. I've been skiing at 8 below zero, and when I got done, my clothes were still soaking wet with sweat. Throwing on a nice warm parka is fine for walking from the front door to the car, but it doesn't work for outdoor winter activity. The layer closest to the skin should be polypropylene or any of the numerous garments that wick moisture away from the skin. This layer should fit tight enough to the skin to wick moisture, but it should not be so tight that it restricts movement.
Skiers have to dress to stay warm, dry and protected from the wind.
If somebody on my team shows up with cotton against their skin, they don't practice. You've just got to keep them clean. The second layer is for warmth. Fleece and wool make good layer stuff. Fleece has the advantage of being lightweight, dry and a capable wicker.