I can not emphasis enough how much MTBing improves people's skiing. My GF start MTBing last summer and we hits trails as well a ton of pump tracks. The first couple weeks at stowe she "got" bumps, it was basically no on snow coaching at all.
I laugh at people who poo poo that sport for whatever reason. There is IMO no better for skiing, and its fun enough that most people once they are reasonable good at it will not need "motivation" to do it. Sure beats the heck out the gym, or running. Also include pump track. Pump track build skiing/MTB skills faster than just riding a bike down a trail, but that helps as well.
I think mountain biking more technical trails/downhills helps with line-finding in snow/bumps. That "vision" for the smoothest path, the body English, countered steering, and confidence to allow the bike to go fast enough to get on plane over the rough stuff, all translate very well to skis and snow IMO. I bought my first mountain bike in 1985 or '86, and was immediately struck by how similar it felt to skiing. In-line too for that matter, but I just can't carry off the neon spandex like I used to in my 20's , plus, I know they don't allow skateboarding on the roads around here, so I assume that applies to in-line as well. Too bad; I've got some vintage Slalom-blades that used to be a lot of fun! Hiking, especially on more technical terrain, has also proven to be helpful for maintaining leg strength and balance, as well as a few early season skins up the W.R.O.D.
I'm lucky to be able to ski 3-5 days a week during the season if I'm injury free, but that's all I do. I'm pretty sure I would benefit from some gym time and cross training, but I've never liked the gym, so pretty much leave the cross-training for after the lifts close for the season, and the roads/trails are clear for biking/hiking. Right now I'm kind of in limbo, with no A-Basin pass, and currently snowing here. I might actually have to break down and buy a day ticket for A-Basin, or start touring again if this keeps up. You should probably all be feeling very sorry for me right about now...