The glideing of skis on snow depends very much of the surface chemistry between the skis and the snow layer which is modulated by temperature, impurities in the snow, wax action etc. at the molecular level. The simple answer is that skis can slide on the snow when the pressure exerted on the snow makes a thin film of water between the skis and the snow. But in order not to have the water/snow stck to the bottom of the skis you need the right kind of wax to faciliate the gliding. The wax acts as an insulator between the ski and the snow/water so that you can glide on it.
When it gets really cold, a different wax needs to be used because it has a different molecular structure to insulate the skis from the snow/water surface. Sometimes I think too when it gets too cold, the pressure itself may not be sufficient to generate the film of water needed for the glide ( think of Boyles law in physics). In any event, it requires the right kind of wax with the right kind of molecular structure to faciliate the glide. That is why it is very important to pick the right kind of wax for the racers - they can loose a race because of the wrong wax used - which normally varies with the temperature and the kind of surface the skiers are gliding on.
When we go to the shop for tuneup they apply a layer of wax suitable generlly for where you are going skiing and for that kind of temperature. However, much of the wax is worn off after several times of skiing (say 7) then you need to rewax. In cold days you may actually have to apply another type of wax.
Similarly during spring when you have wet snow, it sticks to the bottom of you skis if you stand on a place for a long time. Same idea. Without the proper wax, the snow (with water) will stick and the right wax (like red wax or the very soft wax) will help your skiis to glide. Green is I think for medium cold and blue wax is for really colld, I think. But i may have mixed up blue and green. In any event going for a hot wax job at skis shop is a good idea from time to time.
I am not a wax expert but I am sharing with you what i have learned from others.