The reason for knee exercises for skiing and for snowboarding is to build strength and to prevent injury. Protecting your knees is essential for winter sports, particularly skiing - huge numbers of skiers suffer knee injuries each year, and while equipment can contribute to this (over-tight bindings for example), most knee injuries are due to weakness and fatigue.
While that sounds quite grim, the good news is that it's relatively easy with the right knee exercises to protect them from most injuries, if you know what to do. There are two issues you have to address to protect your knees - strength and endurance.
Strength comes from gym work - this should be started at least three months before you go skiing, and will focus on the following exercises:
Performing these three times per week will dramatically increase the strength around the joint, which is crucial for maintaining joint integrity when large forces are applied.
Although the usual prescription is three sets of 10-12 reps, this is somewhat limited. With three sessions per week it would be far more effective to include one strength session each week (4-6 reps of a heavier weight), and one endurance session (15-20 reps of a lighter weight). Mixing these sessions up will give much better all around development.
For endurance, biking is simply the best way to protect this area - the fluid motion is gentle on the joint, but still helps to strengthen it. Other weight bearing activities such as running and stepping will also be effective.
As you will be spending several hours per day skiing, it makes sense to build these endurance sessions up beyond the typical 20 minutes of cardio that is usually prescribed. The longer your training sessions are, the better you'll be able to cope with long days on the slopes.
Now you have a good appreciation of the right knee exercises and why they are important, time to workout with our fitness programs.