Research, research, research. I can't speak to the roads, since it's been 40 years since I was there, but there are resources to give you the info you're looking for. With a rig that size, you will be limited to where you can stay, or even get in to, so reservations will be a must. CGs that can fit you are likely to have full hook ups, though you might want a small generator in case you find yourself having to dry camp. These trailers are meant to be used, so don't worry too much about the wheel bearings. Check your brakes and make sure they're adjusted. Remember that the trailer is supposed to stop itself in normal use; if you feel it pushing you, step up the gain on your brake controller. You also want to have good brakes traveling in the mountains. If you don't have an exhaust brake, OEM or aftermarket, you might want to think about adding one. Makes life a =lot= more enjoyable. When driving in the mountains, watch your temps (water, oil, turbo) and use them to dictate how hard you drive. Don't be afraid to pull up a grade at a speed to keep your temps safe; let the rest of the traffic deal with you as they would a semi. Doesn't mean that you don't need to be courteous and pull over, or off, if you get a load of cars behind you and you can safely do so.
Mountain weather can be highly unpredictable, so be prepared for everything to unseasonable heat, torrential rain and wind to snow. I was in Silverton CO in late July and got snowed on, so have plans in place. Again, this is where preparation is key. That is =big= country up there and there's not always resources when you need them. Personally, even if I never planned on camping outside full hook up CGs, I'd =still= have 2 6v golf cart batteries, just in case. Don't be afraid to hole up for a few hours, or even a day, if the weather turns bad.
Sounds like an awesome trip, but it will take lots of planning for it to go smoothly.
Lyle