Airport Extreme Outdoors?

So it will probably work, and your Airport will probably be fine, but there are certainly some better solutions available to you. Do a google search for ethernet bridge... or check out some products:
HERE or my favorite HERE.

The prices are quite reasonable for what you get, and it will be a far more robust solution.

For the AirPort extreme:

Operating temperature: 32° to 95° F / 0° to 35° C
Relative humidity (operational): 20% to 80%
Maximum operating altitude: 10,000 feet / 3000 meters

You might want to check out a company called OpenMesh, they sell a range of outdoor certified wifi products that I think will work for you. Be warned, any wireless extender, no matter who makes it, will lower your performance... you can pay a pretty heavy penalty. I'd suggest a couple hundred feet of underground certified conduit with an ethernet cable strung between it would be a much better performing option and if you handle the underground work properly, it would be much more reliable too. But, you can do this with wireless, just not ideal if there's any way to run a cable.

If you want to have a look at another (US) supplier, these guys are good:

http://www.hdcom.com/

I used their products to construct a portable link that easily ran .25 to .5 mile. It's pictured on this thread:

https://forums.macrumors.com/threads/1228558/

"geologically challenged" is a nice phrase, BTW. I live in an environment where lava's very close to the surface and often is the surface. So I know what you mean.

Might you consider something like this?

http://cableorganizer.com/cord-covers/high-capacity-covers.htm

These are the first ones I found. Expensive. But my ex-business partner is using something like these -- another manufacturer -- and I doubt that they are as expensive. We routinely ran trucks over his -- not 105 ton dump trucks, but good sized ones. I can find out who makes his.