I would highly recommend purchasing a road bike if you can afford it (any decent one is pretty damn expensive plus all the other shit you can end up buying). I bought one last May, became semi-addicted to cycling, and I have felt like a brand new skier this winter. The benefits (fitness level and leg strenth) are more helpful if you're into big mountain, but it also helped my confidence in the park tremendously because I felt like I could stomp anything and not wash out.
Cycling is also a great way to explore the outdoors because you can cover a lot of ground and go on really long rides once you reach a certain fitness level. I also got bike rollers for indoor training, and these pretty much force you to have really good balance otherwise you eat shit and fall off.