Outdoor recreation or mountain recreation is the normal phrase. People who are passionate about hiking, backpacking, etc. will use this phrase, although it is, as you observe, a little passionless.
More passionate alternatives include mountaineering, mountain sport, alpine sport, and alpinism.
These terms are sometimes used with special, restrictive definitions, but they can be used more generally to encompass the types of activities you describe, so long as those activities occur in the mountains.
Another alternative is adventure sports, which has the advantage of not being limited in application to mountain activities. I am not sure how robust the convention of using this phrase to cover your types of activities is, but it could be used fairly obviously to cover them. That said, extreme sports like skydiving are sometimes called adventurous sports, which might cause some confusion.
Another alternative is outdoor sports, which can pretty obviously be used to cover your types of activities given that outdoor now carries strong connotations of camping, woods, etc. (think of an outdoorsman). That said, the term could also be used to mean any sport played out of doors (for example, football). This might cause some confusion. A similar problem arises for outdoor activities.