This trip sounds like it could be an advanced hike. Is it a photography themed short group hike or something more strenuous that you want to take photo gear along on? If so, the bigger question is what kind of hiker are you and what else are you carrying? What is your pack weight? How long are you on the trail? Will you stop at any camps or places to refill or rest other than trail spots? Are you in good physical condition and have you been training? Have you hiked at that altitude before? Is all of your other hiking/camping gear in place and do you have a good proven system/strategy you've evolved from past hiking experience?
Have you taken any cameras or gear with you before on the trail? How were they carried, stored and protected? What happens when it rains/snows, etc? Are you prepared to lose your camera gear to damage or worse? (I accept the fact that I could break what I'm carrying at any time on the trail. My biggest concern are the pictures, not the gear.)
I am seeing more threads that discuss outdoor hiking and camping that include camera gear. My concern is that folks let packing the camera gear overshadow the more important aspects of hiking comfort and safety. Experienced hikers know what they are capable of and where to draw the line when it comes to secondary items and activities.
My advice is to KEEP IT SIMPLE. Don't take more than one or two lenses. Keep the weight down. Take plenty of batteries because cooler temps run them down. Depending on how cold it is, you might end up keeping the batteries inside your coat next to your body and inside your sleeping bag the entire trip.
Based on the gear you listed, I also suggest that you just take the 24-105. But both the 5D2 and 5D3 are heavy. Depending on what you plan to shoot, you might consider buying a Canon Rebel or SL1 with a kit lens and save yourself a lot of weight and worry about your heavier more expensive equipment. (I recently took an SL1 + Tamron 18-270 lens on the trail for over 10 days and it worked well for my needs.) Or get a Powershot like the SX50. The easiest thing to carry is have a Powershot D20 hanging from your pack strap but I realize that is a huge compromise compared to an SLR.
Whatever you do, PRACTICE, PRACTICE!! Take the gear with you on hikes before the big trip, use it and see how it all works. How does it feel on your pack, how does it swing, does it get wet, how do you deal with it when you take off the pack, sit in camp, walk places, sleep, etc. How are you carrying your drinking water? When you drink on the trail, will it spill on the camera? How will you deal with humidity? Dust? Dirty lens? Will you have trekking poles? If so, where will the poles go when you want to shoot pictures on the trail? If you are with a group, they won't want to stop every few minutes and you won't want to keep handing others your poles, etc to use the camera.
Sorry if you are already a seasoned and experienced hiker but if you're not, I don't want the trip to be a bust because you haven't considered all the aspects of carrying camera gear on the trail. I want you to be safe and not put yourself or others at risk. Taking heavy extra gear on the trail is not as simple as it seems. Or maybe I just have ultra high standards for my own comfort and performance. At any rate, I sincerely hope you have a great time!