Everyone is going off on the humidity - that's the least of your problems. Assuming that it's a non-condensing atmosphere (i.e. fog), the warmth in the box will keep any additional condensation from happening and the box will run fine.
High temperature may be an issue. I live in Phoenix, and putting a server outside is, well, not the worlds best idea. If you live somewhere where the high temps in summer are less than 90 degrees, you're probably fine from a temperature standpoint.
Bugs and dust will be the big problems. Solve those, and you'll be good to go.
I've built boxes before that housed computers in my garage. I made'em out of plywood, made them reasonably airtight, and put muffin fans on one end, pulling outside air through a high-quality air filter (http://www.amazon.com/20x30x1-19-5x29-5-Filter-Furnace-Filters/dp/B00GBJIENE), and put exhausts (wire-covered) on the other side. Worked fine through several summers where the garage got up into the high 90's, didn't have any problems with bugs or dust or component failures.
The two or 4 disk NAS boxes are a great size for this kind of thing. My current home server is an ancient 4-bay Buffalo Terastation case, that I ripped the motherboard out of and replaced it with a low-power 12-volt motherboard (ASRock Q1900DC-ITX) and installed FreeNas on it. Works great, and something like that would work remarkably well for your needs.
Good luck, and don't listen to the crybabies.