Yea this is kinda a "fail" imo. I haven't been able to store anything in containers anywhere, and I've tried several different types.
My Nord barbarian was forced to throw all his armor on the floor of his bedroom in the Inn at Riverwood. He likes walking around in normal clothes when he's in town. Anyways, he can't store all this stuff, so he throws it down, and then some NPC walks up to his room and says "hey, are you trying to get rid of all that stuff? Mind giving it to me?" or something. At least the game gave my Nord a chance to say "Yes" or "No", but yea, that is a bit faily that he can't store stuff
I think you aren't supposed to consider storing stuff. You have to buy a house if you want to put stuff in it you will never touch again.
That's
fail. In Oblivion and I'm assuming Morrowind, stuff could be properly contained in actual containers. The fact that Skyrim is not the same isn't game-breaking, but still a fail.