I keep primers inside, with the dies and press, since it's not too likely they would cause any kind of grief.
Powders stay out in an unheated (or cooled) garage, in their original containers.
Never had a problem.
And we get both a dry and a wet season, each about half the year.
One powder, in a one pound container, is a version that doesn't get used any more, and must be twenty years old.
But it might, one day, so there it sits.
It's still ok.
Lock the doors, they're coming in the windows.