First and foremost, I am by no means a "mountain" hunting expert, and there are many on here that have done way more than I have, including a few that are posting on this thread so I defer to them for sure. I have done a few backcountry hunts including mule deer and elk in Utah, and Dall sheep in Alaska. Last year I went to the Mackenzie Mountains of the NWT of Canada and hunted the big moose they have there as well as mountain caribou. This year I am headed to northern British Columbia to hunt Stone's sheep and Rocky Mountain Goat. My 2 cents is the following:
1) When I think of a mountain hunting rifle, the first thing I think about is weight. I used to think that it was all BS, and didn't really put much stock in the theory that 1-2 lbs could make much difference. However, after hunting a few times in the backcountry, and having to lug my big behind, a 40-50 lb pack, and a fully loaded and scoped rifle up some extremely steep and rugged terrain, I do think some consideration should be paid to the idea of a lighter than "normal" rifle. How light is enough....only you know the answer. But I can tell you that after a few days of being wet and cold, and absolutely dog tired from climbing for hours only to find that the buck, bull, ram, etc., is not quite what you thought it was, and you are going to have the pleasure of doing it all over again the following day after a long and arduous descent down the mountain back to spike camp, etc.,......weight starts to become a factor to me....at least mentally...and you will find yourself trying to find ways to shed those few ounces to lighten up your load. I've even found myself contemplating a pack strap or buckle and seriously considering tossing it only to save half an ounce. So given the choice between a light rifle and a moderately heavy rifle, with all other things being equal, I'm taking the light rifle each and every time.
2) The second thing regarding a mountain rifle I think about is construction and build components of the rifle. For you, I'm not sure if cold and wet are as much a consideration as say a sheep hunter in Alaska or Canada, but the terrain your going to hunt is rugged and the rifle is going to get banged up. As much as I prefer a beautiful piece of figured walnut and blued steel, I feel that type of rifle is just not as practical as a synthetic stocked rifle with a thinner than average barrel, and a weather resistant coating like Cerakote for instance. Wood, when wet, can swell and thus alter your bullet's POI. A wood stock can crack or break easier than a synthetic one. And on and on and on......
3) Optics is another very important consideration. Both weight and light gathering capability come into play here for sure. So much of mountain hunting is an optics game. From the time the quarry is spotted miles away to the final approach and stalk, optics play a huge role in hunting mountain species. There are plenty of great rifle scopes out there, and for this type of hunting, I think the adage of "you get what you pay for" certainly holds true. Trying to save a buck on a cheaper scope is probably not the best strategy, and so in my opinion, if there ever was a time for premium/alpha glass it is now. Alpine species tend to hide out sometimes in the nooks, crags, and crannies of the mountains, and shadows come into play for sure, so the ability of the glass to gather and transmit a lot of light clearly is really a plus. As far as ballistic reticles and turrets go, I personally feel that they do help when shooting at objects at over 300 yds (meters) but the caveat is that you have to practice with them, and have a method to accurately range the animal in question. I'm with other posters when they say know your limits as to what range you can consistently hit your target at from field conditions. Personally, I rarely take shots at over 400 yds. because I can't routinely practice beyond that range, and I feel that there is so much that can happen between the time the bullet leaves the muzzle, and when it impacts the target past 400 yds. One day, I'd love to get more proficient at shooting at targets past 500 yds., but currently I don't feel comfortable doing that.
4) Finally is caliber, and the reason I left that for last is that personally, I don't think it matters as much. There are many flat shooting calibers out there that are great. Certainly, I think there are some reasonable limits, and so no, I don't think trying to take a poke at a Marco Polo ram at 600 yds with a 45-110 black powder Sharps rifle, is reasonable...at least in my hands, but certainly a 270 Winchester, 308 Winchester, 30-06 Spg, 300 Win. Mag., etc. have all been proven to be great mountain cartridges. You mentioned the 30-06, and I would think at the ranges you have specified (</= 450 yds.), a 30-06 Spg with 150 grain bullets at close to 3000 fps (some of the factory Hornady Superformance ammo supposedly achieves this velocity) would be a great mountain cartridge loading. I was reading an article in Sports Afield the other day where Craig Boddington was debating the age old question of which is a better cartridge between the 270 Winchester and the 30-06 Spg. One thing that interested me was that the legendary Jack O'Connor himself (270 Jack) who has killed way more sheep than I ever will even dream of killing, took most of his rams with a rifle chambered in 30-06 Spg. (earlier days of his sheep hunting career), and even privately admitted that the 30-06 Spg was a more versatile cartridge. I think the great thing about the 30-06 is the versatility of the loadings. You could zero your scope for 150 grain bullets to hunt mountain species, and then turn around and re-zero it with 220 grain bullets to hunt big plains game animals. You also mentioned the 270 WSM, and in my opinion, if there ever was a near perfect "sheep" cartridge to be utilized in a short/compact, and lightweight rifle, the 270 WSM might be it. However, if you're not a handloader, and factory fodder is not readily available where you live, then it probably doesn't make much sense to own a rifle chambered in that cartridge.
If it even matters, my personal "mountain" rig is a custom rifle built off a Remington 700 clone action (Stiller Predator) in 280 Ackley Improved. It has a lightweight contoured, fluted stainless steel barrel at 24 inches. It sports a Manners EH3 Lightweight Stock, Timney trigger, and all the metal is Cerakoted. I topped it with a Swarovski Z5 3.5-18 x 44 with a customized ballistic turret for my handloads. Fully loaded, scoped, and with a sling it comes in a little over 7 lbs if I remember correctly. I'm shooting a 140 grain Nosler Accubond behind Hodgdon H4350 at arround 3200 fps. It is a very accurate load (<0.5 MOA if I do my part) in my rifle. Do you need a custom rifle dedicated to strictly mountain species? Absolutely not. But if you are inclined to have a rifle built specifically for mountain hunting, it gives you an idea what you can have done. In my mind, I know this rifle will shoot better than I can, so if something's amiss in my practice, I know more than likely, it's me. It certainly is a confidence builder.....
Again, my 2 cents......if it's even worth that much....
Good luck in your search, and let us know what you decide on.....