A summary of likely answers:
1) get what I have, as only that will take decent pictures.
2) get what wins all the popularity contests and (past) sales figures (strangely, d*g*t*l not allowed)
3) get a camera which will hammer nails, can be used as a weapon and will attract notice because of it huge white lenses
4) get a camera with as many "features" as possible: you never know when that 1364th nose-activated reenforced Plutonium AF sensor will win you a prize-winning picture. Also, shooting at 10 FPS is almost as good as watching a super-8 home movie...
5) ridicule any non-mainstream cameras (meaning 99% of the general public hasn't heard of them) such as Leicas, Soviets, rangefinders in general, ect.
6) that older mechanical cameras are too unreliable and innaccurate to use, that the "battery problem" is unsolvable...
So, more seriouly now....
I also go mountaneering and on long-distance treks, so the kind of issues you have are familiar.
First, the cameras you mention:
Nikon F3: a bit heavy. Also, not having to rely on a battery (or change one in awful conditions) is a plus.
Rollei 35S: Great lens. You're stuck with a 40mm FL. Scale focusing might not be an issue in your case, as you don't seem to do many closer-ups.
Leica III: No meter. Neeeds extra viewfinder for FLs other than 50mm. Probably needs a CLA. Slow lens changing.
Bessa R: Nice choice, except for fine-focusing fast lenses or teles.
I tend to favour a lighter & more compact SLR or rangefinder system.
My "mountain SLR" is a Rolleiflex, but you could look into Olympus OM or Pentax MX cameras. In the Nikon world, FM, FM2, FM3A.
A rangefinder can be even more compact and slightly lighter, and its disadvantages minimal (I rarely take a 200mm+ lens with me on a long trek anyway).
Some examples of weight:
Leica M6 + 21 +35 +90 1080 g. (1274 with a 15mm included) - A Bessa would be somewhat lighter
Rolleiflex SL35-E + 18 + 35 + 85 1326 g. (the 18mm isn't expecially light)
Nikon Fe2 + 20 +35 + 105 1579 g. (the 105mm is pretty heavy)
Pentax 6x7 +45 +75 +165 3789 g. (with meter prism).
Iskra 6x6 (one of the best MF folders around, results-wise) 918 g.
P.S: I mentioned MF because nowdays you can get a MF enlarger almost for free and the Iskra really is sweet & relatively light.