Lots of good advice. One other thing I'd stress - gym time, and cardio-specific stuff is great, and it really does help a lot. But in my experience, structured workouts are only part of the equation when it comes to preparing for extended travel in the mountains.
I led wilderness expeditions for 12 years in some pretty remote parts of the Americas (Alaska, B.C, Wyoming, Chile, etc), and I saw many people who were very physically fit - highly competitive marathon runners, and such - crumble on long days in the mountains. There is a world of difference between being tired, miles from camp, late in the day, in a whiteout, on an exposed scree slope with heavy pack, and being in the gym, no matter how intense your workout regimen might be.
Workouts definitely help, but I'd also strongly suggest getting out and traveling in uneven, steep terrain, in less than ideal weather, etc. whenever you can, if you have it accessible. Bike, ski, hike, year-round. Just as target shooting is only an approximation of hunting, so are structured indoor workouts in comparison to extended time in the mountains. And there is a mental "toughness" component that requires regular workouts as well, and that often seems underestimated.