Last year I came into ski season fairly out of shape. I'm trying to avoid that fate this year. What cross training activities should I be doing that will pay off during ski season this winter? Trail running? Mountain biking? Yoga? I'm a new dad without a ton of time, so trying to find something I can do 2-4 hours/week.
You didn't say what type of skiing you do, so I will reply to this as if it could be any. For myself, I do all types of skiing (alpine, backcountry, XC, nordic skate). I find that a combination of cycling (both on and off road) and running during the off season is a great way to stay in shape for the ski season. It isn't a perfect science, however. For example, I still find that my quads need a bit of extra work when I start the season again, but a few weekends of skiing usually bring those up where they need to be. If time is a factor, you can easily take a few spin classes and run in your neighborhood.
If you backcountry ski, another idea is to hike with a heavier pack during the off season. If you are a nordic skater or XC skier, you can also get roller skis and use those around your neighborhood when you have time. It's a lot of fun and can be a good conversation starter with the neighbors 😉
In general, I find that if I keep my cardiovascular fitness up, it sets me up with the right foundation when the ski season starts. Trail running, mountain biking, road cycling, etc. are all great ideas (and a bit of yoga too to help stretch what will certainly get tight as you increase your activity level).
I admit it - when spring hits I'm a glutton. I tend to make up for all those months of working out for ski season and I usually pack the pounds back on pretty quickly. But come late summer I start watching my diet and exercising again. I don't have the time or space for a lot of equipment so my go-to is the elliptical machine at home. It gets my cardio going and after being back on it for a few months my legs are in prime shape. It's actually kind of nice to be exercising while being able to catch up on a few tv shows or movies.
It's not too late. I love the Mountain Tactical video above. I'm a ski patroller and after one particular season of getting absolutely destroyed at the beginning, I started Orange Theory the following Fall. During the pandemic, it's essentially free on line. Their 30 to 50 minute workouts helped me with both cardio, core and lower body strength training. It's made a huge difference to my ski season.
I ski all winter myself (Alpine and Nordic). I have found that inline skating and roller skiing in the summer keeps me best prepared for the winter. Easy to do around the neighborhood for as short or long as possible. Use a headlamp and head out after the kids are in bed if need be. Use a stationary bike or treadmill for the bad weather days. Nothing like inline will keep you as prepared for alpine ski season in terms of muscles used, balance, etc. It is practically the same motion as alpine, plus even moderate hills on inline skates can be fun/challenging. Rollerblade even has a free skate to ski training guide. I prefer a 90-100 MM wheel diameter with 84-88 durometer and a soft boot for inline skates, use manufacturers recommendation for roller skis. Rigid boots are more like alpine ski boots, but the soft boots have enough support that comfort/breath-ability outweighs in this regard. Use with or without poles, but be sure to get special tips for pavement if you do use them. If you want to go real extreme there are even offload pneumatic inline skates for the trails, but they have a very steep learning curve.
I also agree with the other posters that cardio is key for ski season and add some leg weight exercises if you can.