The 6.2 is a good dependable engine. I have one and pull a 5th wheel with about a 10,000 gvwr but I haven't ever weighed it to see how much it weighs loaded. I have had it in some fairly steep hills in the eastern US but not over the Rockies. I'm sure it would do the job through the Rockies but I'm sure the altitude would pull it down. It will drop down to 3rd gear through the steepest parts and it runs some fairly high rpms but nothing that will hurt it.
The only negative I have with it is the fuel mileage unloaded. If you're going to drive it very much unloaded be prepared to spend a lot on fuel. It does not get great mileage loaded but I figure that's to be expected with just about anything.
It would really depend on how much you want to tow as to how good it will do. If it were me and I were buying new I'd probably buy a 7.3 F-350 if I wasn't pulling a huge trailer. That's just me and everybody has a somewhat different opinion.
Can you get a 10 speed behind a 6.2. If you could that would help.