That burn is, or so the exercise scientists tell us, due to the accumulation of hydrogen ions increasing the acidity in the muscles. Those ions come from this disociation of lactic acid in lactate and that hydrogen ion. This occurs when you are overly reliant on glycolytic metabolism for the exercise. You are exceeding the aerobic capacity of the muscles involved and are beyond the anaerobic threshold if you feel that burn. Yes with proper training it will go away. You will be able to ski or run up hill faster before feeling that burn. That is what aerobic training is meant to do. If you do a high percentage of your training where you are feeling that burn then that is why you feel the burn. You need much more aerobic base training and you need to ski/run up those hills slower.
Scott