Well, there is hiking and then there is mountain climbing. I'm guessing that you're going to be doing hiking ... which doesn't usually involve pulling yourself up the side of a rock face using your hands. As such, your hands should be fairly free to shoot most of the time, but you won't want your camera dangling from your neck on those moments you DO need to bend over a bit and grab a rock for balance.
You'll want to keep your weight down, so one lens is a good idea... or perhaps one zoom and one wider-angle fast prime. I usually go with my Kit zoom plus an older 28mm f2.8 manual focus lens.... which is surely going to be used for landscapes and autofocus isn't that much of an advantage.
During my hikes in the Arizona desert, I carry my camera out in the open, but slung diagonally. And on my back, I carry:
3 liters of water
Fruit and food appropriate for the length of time
Monopod -- Since there are lots of slopes to contend with, sometimes the best angle requires support from a rock that is a couple of feet lower than the ground I'm standing on...
Rotating polarizer filter
Bulb brush
Spare charged battery for my pentax
One highly reflective car windshield sun blocker (In case I get stuck WITHOUT shade OR in case I need to add some reflective light to something that is deeply shadowed.
Sunscreen
pocket knife
two 52 inch shoe laces (in case you need to McGyver a tourniquet)
and... depending on WHERE I hike... anti-venom
Have fun, and make sure your friends DON'T give up on their resolution!