I do almost all of my hunting is in the North GA mountains and I've hunted the mountains of Colorado a few times. The mountains are just as steep here in the east and just as rugged. The only difference is that I'm at 3000-6000' elevation here and 7000-12,000' in Colorado. It has always taken me 2-3 days to adjust to the altitude in the west and after that there isn't much difference.
A backpack hunt into one of the more rugged areas here way back in 1977 made a huge impression on me that I didn't want to lug around un-necessary weight. I chased light " Mountain Rifles" for a long time. Including a couple of Remington Mountain rifles.
But I also found that it was possible to have too much of a good thing. The Remington Mountain rifles and the Kimber I used to own were feather light, but that light weight made them harder to shoot accurately in the field.
Some criteria that I've settled on.
#1 I don't want a pencil thin or short barrel like used on many rifles. I want a full length 22"-24" barrel with a standard or maybe even a light varmint contour. The weight reduction needs to come from somewhere else. I do have a rifle with an 18" barrel, but it is my brush gun, not what I call a mountain rifle.
#2 After the 1977 hunt I started exploring lightweight synthetic stocks and settled on a Brown Precision in 1983. I haven't hunted with a wood stocked bolt rifle since. The better quality synthetics will save 1/2 to 3/4 lb plus they are tougher and more stable in changing environmental conditions. Most factory synthetics don't save you any weight, some do, so you have to choose carefully. Today I have some factory synthetics, but have McMillan Edge stocks on my go-to rifles.
#3 You can save a lot of weight with optics and mounts. MOST steel mounts will weigh 6-8 oz. The Burris Zee rings are pretty lightweight steel and a good choice. I like Talley Light weight mounts coming in at about 2-2.5 oz. Scopes matter too. I don't need more than 3-9X40 and there are many options in the 11-15 oz weight range. Many scopes, especially those with more magnification will weigh 18-20 oz.
#4 A short action rifle with everything else being equal is about 1/2" shorter overall and about 4 oz lighter. I've found that a 308 does everything a 30-06 does with less recoil in the same weight rifle. Or about the same recoil from a rifle 1 pound lighter.
#5 Some rifle actions are simply much heavier. Everything else being the same a Weatherby is about 1/2-3/4 lb heavier than a Remington. Fluted barrels take off 2-3 oz. without hurting accuracy. Not enough that I'd pay to have it done, but if buying one already fluted something to consider
#6 The cartridge is still personal preference. 6.5 CM, 7-08 and 308 would be great choices with plenty of reasonably priced ammo. But if someone just wants something else they will all work. Some guys prefer the long action 30-06 class of cartridges and others are good enough to shoot far enough to use a magnum.
None of those weight reduction strategies look like a lot individually, but all combined can make 2-3 lbs difference in how much you're carrying.
I've found somewhere between 7-8 lbs scoped is about right with 7 1/4 to 7 1/2 about perfect. I'd say 7 lbs is about the minimum. My Kimber was under 6 lbs scoped and just too light. A 7-7 1/2 lb rifle is light enough to easily carry, but with enough weight to shoot well. If I felt the need to go with a magnum rifle it is harder to get them much under 8 lbs and still be shootable.
On a budget I like the Ruger American rifles. Out of the box a Tikka T3x is about as good as it gets. But my personal "perfect" mountain rifle is my McMillan stocked Winchester 70 EW in 308. It's 7 1/4 lbs as pictured.