>>2161567If I had to simplify it, I would say the three biggest costs, in no specific order, are:
Gear
Travel
Guides/classes
I know /out/ will balk at this, but for mountaineering, especially winter mountaineering, go with a guide. Take a class, get with a guide, let them teach you. Their experience and knowledge is invaluable. Let them teach you the essentials of footwork, route navigation, emergency shelter setup, rope work, etc. There are dozens of ways that your simple and untrained mistakes can lead up to you injuring or killing yourself. The first two winter mountaineering courses I took were about $900 each, and I had to drive about half a day to get to them.
Which brings us to the next major cost. Travel. You're quickly going to find that the best places you want to be at, are a plane ride away or a one/two day drive if you're lucky enough to be on the West Coast. It's going to eat up all your work PTO. At one point I met a dude that lived in the Midwest, and he was flying himself and his gear out to Oregon, Washington, and Alaska, to do climbs. I can't imagine what that would cost after awhile. To me it's the kind of hobby that, if I left the West Coast, I'd drop it completely. This doesn't even get into international travel either. I knew one guy that did that. He said it was affordable, and I didn't ask what it was like, because my paycheck and work life wouldn't handle that kind of stuff.
And of course, gear. Like
>>2161598 said, you're combining backpacking, climbing, alpine hiking. You can't skimp on your clothing or your sleeping gear, because it will get miserably cold at night. The cost of rope(s), harness, draws, sling(s), clips, screws, boots, clothes, ice ax, poles, handheld GPS, sleeping bag, liner, sleeping pad, foam roll, all of that adds up. I excluded a bunch of stuff there.
It's the most fun thing I've ever done. Mountaineering feels like the natural evolution of outdoor hobbies rolled into one. It's challenging and very rewarding.