Yes, of course, but the problem is power: how are you going to store enough energy in the spacesuit to provide both heat and pressurized air? You'd need to be

Yes, of course, but the problem is power: how are you going to store enough energy in the spacesuit to provide both heat and pressurized air? You'd need to be tethered to a good-size generator or something. You'd also need a LOT more power than used for real spacesuits, because of the heating requirement. In space, you don't need much heat to stay warm, because there's no way for the heat to leave your spacesuit other than by radiation, which is horribly ineffective (and that's a good thing for keeping astronauts warm; it's not such a good thing for keeping your electronics cool though). Climbing a mountain, there's still plenty of air, even if it's thinner than what you're used to, and that means you'll have convective cooling, which is extremely effective (notice how it's used in convection ovens, where they blow a fan to improve the effectiveness of the heating). So your spacesuit will need some really serious insulation, and still will need to generate a lot of heat to replace the heat that's continually being lost to the the ambient air. On top of that, you're not floating around in space, you're climbing a mountain, so the spacesuit needs to be very rugged. Of course, tearing it won't cause immediate doom like in a spacesuit, but it's going to make it much worse to have cold air streaming in, and losing your pressurization. IMO, the whole idea of climbing one of these mountains seems unnecessarily risky and just plain foolhardy to me. If you want to see nature, go hike a nice mountain trail in a temperate climate, where you'll see greenery, trees, maybe wildlife, etc. There's nothing to see on Mount Everest except a lot of snow, rocks, and corpses, and there's a significant chance your corpse will be added to those. AFAICT, the main reason people do this is for pure ego, nothing else. That's why they walk right by people who are dying on the slope instead of stopping to help. Utterly disgusting.