This.

Sounds like you are planning on finding stairs and training on them which is the best training for stairs.

Riding will give you a good cardio base and hill climbing/repeats etc. will help you with pacing.

My GF is a strong cyclist/runner (plus she uses one of those stair steppers that is a conveyor belt of actual steps) and almost never has leg pain when we go snowboarding. Last year she started doing the stairs near her work (Seattle is full of long stairs) for an hour workout going up and down. The first few times she could barely walk the next day. Going down a lot of stairs or steep trails really works your legs in a different way than almost anything else.

I can't tell you the number of stories I've heard (or witnessed) of people attempting Mt. Rainier and getting whipped who were really fit, strong runners (a lot of them marathoners). For something like that there is no substitute for long, steep uphill hikes preferably with weight.