Just a personal opinion on "off season" training from the mistakes and "ah-has" I have gleaned over the last 20 or so years. By no means am I trying to tell people what is right or wrong, but just a personal opinion on what works for me....
Skiing is very hard on your body, and tends to stress/strengthen very specific muscles and movement patterns. I agree 100% that pre-season training can make all the difference in the world to both prevent injury and give you a jump-start to your year, since you just can't get that kind of strength doing any other sport.
However....
Pre-season is not the same as "summer" training. I'm a big believer that the body responds very favorably from an extended break from seasonal sports. "Extended" could mean anything from 2 weeks to 3 months (or more). I used to struggle to maintain my ski fitness all summer to be ready for the next season, but I've found it's actually much more detrimental to keep pounding those muscles into oblivion. I like to put away my ski stuff and forget about any ski-specific training until late Sept/early Oct. It allows my muscles to re-balance (skiing can lead to some really crazy muscle imbalances). Hiking, biking, running tend to work my hamstrings way more than skiing, and have a totally different movement pattern. I also like that mountain biking tends to share the same weight-shifting and body-awareness concepts of skiing, so it keeps my "downhill eyes" in shape.
The beauty of this concept is that it allows you to really hit your seasonal sports hard - ski hard in the winter, run/bike/whatever hard in the summer. You don't waste your time trying to do dryland ski training all summer or indoor bike training all winter, and it gives your body a chance to recalibrate every 6 months. It's a built-in method to avoid overuse injuries. Or, it allows you to just have fun on your off-season, doing whatever hits you on a whim all summer without worrying about TRAINING. Plus, I get super-overstoked in the fall to start ski training if I haven't been doing it all summer!
Granted, if you're a professional racer or something of that nature, it requires you to stretch your training season much longer than, say, what I would do. But even the pros take long periods of time off in the off-season.
So, bottom line - try some yoga, swim, run a race, learn to mountain bike, go on a river trip, go hiking, backpacking, whatever, as long as it's not skiing-related this summer! Your body and mind will thank you, and you will be double-excited to get back to it this fall.