In adding foot steering to release the outside ski from wet snow and get a tighter turn than carving could get me, my foot started to cramp.
I focused on what was happening and realized that I was pushing my heel out to twist my foot, this was putting real stress on the side of my foot.
Try this; with your feet up on an ottoman or the like, bend the toes and forefoot of your right foot to the left. You can feel the strain on the outside area of the foot, it does bend.
The solution for me was to focus on femur rotation to add some torque to the ski (feels like knee angulation) instead of foot steering and the pain went away.
REASONS FOR ARCH PAIN:
1. Tension in the foot cause by trying to "grip" the snow with your toes. Solutions; wiggle toes, raise toes up.
2. Pressure on the balls of the feet from driving the tips of the skis in with the feet. Solution; get the tip pressure from higher up the boot, from your shin on the tongue of the boot.
3. Pushing the heel out and thus bending the foot. Solution; get that extra torque from your hips (or legs or knees.)
4. Weakness in those small muscles in the bottom of the feet; Solution; exercise them. Put a towel on the floor with a weight on it and pushing down on it with your toes, pull it towards you.
5. Bottom two buckles on boots too tight. Solution; loosen
6. Boot adjustment, footbeds, or new boots needed. Find a good boot fitter. The problem could very well be in your boots, and even if that's only part of it - it will help.