I'm familiar with your problem, although more because I always end up skiing a lot in the early "on-snow" season without having done an adequate amount of ski-specific training. I end up with that sore knee thing because my lower leg muscles aren't really in shape and they are basically over-stressed. The icing is just one component for remedy.
Zach H. touched on a very good point: you need to classic ski to balance your skiing (and skiing physiology). Mainly, classic will help to strengthen the lower leg muscles and increase your balance capabilities. Get one or two of those balance cushions and do some one-leg exercises on them to increase your lower leg strength and just all around proprioception -- you can also do these without the cushions, but they increase the effect by a huge factor.
The knee pain is usually a transmitted pain that is actually coming from the extreme tightness and "banded" nature of the lower leg muscles: peroneus and tibialis. You need to get a foam roller or rolling stick and go to town on massaging them to soften them up and get blood flow. This will need to happen a couple of times a day. You gotta go deep in there to really soften them up. When they get "banded," they will transmit the pain into your knee, where they are attached...this happens too long, and you will have tendonitis. Sitting or standing in a bucket of ice-water up to your thigh is better than just applying an ice pack. It will get rid of all the inflammed areas from feet to knees, which is all connected and contributing to the knee pain.
Finally, a regular stretching routine each evening will also help alleviate the tightness that results from skating. Be sure to incorporate all parts of the legs: hamstrings, IT bands, quads, glutes, lower leg in multiple directions (peroneus is on the sides, tibialis is in the front). Feet and calf muscles are also important. Do it before bed or before dinner and make it a habit. Look up stretching routines on the 'net or get with someone who knows about it.
You hear a lot of BS about do/don't stretch at night, but take it from someone who has been an athlete for a very long time: stretching at night is very beneficial for recovery and injury prevention.
Good luck!