I just started knapping a few months ago, so my stash is somewhat smaller in scale. Right now it's in a 5 gallon bucket in my shop but I can see that at some point it will grow beyond that. I've got a "big ol barn" (see El Destructo's post on what he learned while in Texas) that will hold lots of rocks and never be in the way.
I think just so long as it's protected from the freeze/thaw cycle and ice wedging, you should be OK with it outside.
Mike