I store mine both in and outside. Never have had a problem with it.
When I lived in Ohio (a very long time ago) it was normally the humidity that sometimes played a little havoc with me when sometimes I would get some chunks in my powder horn or can, but some shaking of either one brought it right back to a usable condition and I don't believe it effected my accuracy,,, least I don't recall it doing that.
Since living in the northwest part of Nebraska for the last 30 years (give or take a year), I've not had this problem regardless of where I store my black powder as our humidity here, is nothing like Ohio's humidity. We have it, but not to the same long extended seasonal periods.