I am planning a hike with some RPG friends for the Summer, and looked into a rules lite RPG playable while hiking (or resting during the hike).

SHERPA seems to fit the bill well. Character sheets fit on the size of a business card (the other side can be a brief review of the system mechanics), luck points are small rocks you can carry or slipnots on a lanyard. Randomization is done using a stop watch which basically produces a D10 with the tens/hundreds final digit (0=10), and the basic mechanic is roll under the Attribute+Modifiers you have for that action. 

It's a pretty simple system that looks like it will work. But I am curious if anyone has played it?

I'm also curious if anyone has other suggestions for a game which could be easily run while hiking (or resting during a hike).

I think we experimented with Sherpa once or twice in the 90s. I don't really remember much, but I think we just gave up on it as pointless. I did like Steffan O'Sullivan's style, and his posts on the game were engaging, but that and other ultra-minimalist games really convinced me that, at some point, you might as well go full-blown narrative and create a shared story on the fly, instead of pretending the mechanics mean anything. You can always randomize things by looking around or making quick little predictions of what you'll see next. And it's simple enough to give characters a couple broad player-defined traits (steal from OtE, Risus, or even Fudge, for instance), and just adjudicate based on what seems reasonable (Amber's system where the higher score always wins, unless you can come up with a creative way around it, works fairly well).

Any game works for this until you hit combat. A friend of mine and I used to hike around when teens and spend all day roleplaying.