Balance being the one most important skill, here's some ideas to improve it before or during ski season.
A good approach would be to be active in a few related sports that build balance (mountain biking, tennis). Two months before ski season, I start to get in shape and I also pull out my balance board and spend 5-10 minutes daily on it.
Using a balance board is a very easy way to work on your balance. Use a variety of two footed and one footed exercises on a balance board frequently.
There are many similar devices to work on your balance, use as many or as little of them as you want... but don't expect your balance to improve rapidly if you don't work on it. Especially with age!
Here are a lot of ideas:
Bicycles improve balance. Especially mountain biking. Skating is awesome, quite obviously. Don't think just "static balance" but dynamic balance: tennis is an awesome sport to develop ski skills.
Do any or all of these, as much as you can or as much as you need to improve your balance.
Racer could benefit from these...
Squats on a medicine ball:
Your balance skills depend on your overall shape, so keep in shape. Not strength or endurance necessarily (although on long ski days or difficult terrain, these come into play), but just being in shape.
Having a strong core and legs is very important - See Fitness++ for more ideas on working out and improving fitness.