depends depends depends..
What size quarry, what average distance, what 'type' of mountain! how steep, how flat, etc. Is it a scottish hill/mountain with rolling heather and a few crags, or a swiss mountaineering job! is it a nz mountain that's fully forested?
There's no such thing as a 'mountain rifle', there are rifles which have certain characteristics that IMHO make them better for mountains.
Firstly, let's take Scottish highland/hill out of the equation here, that's in 99% of instances not a 'mountain' (yes, someone will chip in with a picture of a rough mountain in the highlands where they stalk, but let's look at the norms). The reason I remove this category is because it should be under 'hill rifle', not 'mountain'.
so, a mountain rifle, in my book should exhibit some of the following features:
1. be suited to the largest game you are likely to hunt
2. be a calibre and rifle you shoot comfortably with in all positions without flinching
3. Assuming large bear is not on the menu, a 'reasonably' flat shooting calibre 'might' be an advantage for point and shoot to 300; however, zeroing at MPBR and limiting yourself to that, and/or having turrets and range finders for anything 'over' should make ballistic profile redundant.
4. Looking at the vast majority of 'mountain' game species, 7mm through to 30 cal are the most sensible options for 'all rounders'.
5. whilst 7mm RM is a great rifle, to get the most out of them you need 26"-30" barrels, therefore, I would write them off and go with a round which works admirably in 20" to 24" barrel length. I would therefore seriously consider 7x57, 7-08, 7x64, .270, .308
6. If you travel the worlds mountains and need ammo available locally, 7x57, .270 and .308 are suddenly becoming the favourites (although of course some places will readily stock the other calibres ammo).
7. Stock wise I would wish for a european hogback style or griffin and howe straight slant comb with same drop at comb and heel as hogsback, these make the best rifles imho for shooting sitting, off sticks, standing and sitting behind a boulder, etc. etc.
8. I would go with pistol grip that's not too steep for better and swifter handling, as well as a reasonably thin front end in either a curved tip or schnabel style
9. good wrap around checking in no smaller than 18LPI is a must for grip in rain and sweat.
10. a great canvas sling (wide) that can be adjusted and spun a turn anticlockwise for a quick fit around the left arm (assuming RH shooter)
11. decent QD mounts such as recknagel eramatic, eaw, smithson or clawmounts are a must
12. 2 leaf rear sight and a nice tall visible front sight bead such as a white insert partridge sight, a hood is not a bad idea if you risk slipping on rocks, and then a banded sight is best for sturdiness. same with sling loop, banded.
13. sigts regulated at 75 and 150 yds, personally don't know anyone taking game at 300 with iron sights! that's just for show to have on your rifle...keep it real.
14. a floorplate...no magazines! seriously, magazines that can fall out on a day(s) trek into the mountains,, no no no
15. trigger - KISS IT!! keep it simple, nothing fancy, something sturdy that breaks right for you, nothing that fails with a bump or knock or a bit of water/humidity or dust. something like Dressels or Alaska Arms please.
16. Action..ok, I'm biased, Mauser 98! works works works, and can be stripped (bolt) and cleaned in the field in minutes. nothing more to be said.
17. barrel profile - for gods sake, keep it light!
18. bipod - oh dear, use the land and your daysack
19. anything else,,,I'll be back when I recall
something not entirely far from this except I would opt for 2 leaf rear sight and a floorplate with a trigger guard based lever, maybe a 3-9x36 scope, that said, you can't beat a zeiss diatal c 4x32!