Agree with PP, plus how deep are the containers? I assume for privacy you want tall plants, which generally need deep roots.
But you also can try heuchera if there isn't too much sun, and you may manage to get ice hardy pansies to make it a long time.
I like your option of short variety of native grasses, which will have dried winter interest and may re-emerge in spring if the roots can have enough room. See if pansies will survive among them for color.
Generally, it will be a challenge, but try choosing drought tolerant perennials that are hardy two zones north of you, like dianthus, yarrow, Christmas fern, nepeta, Woods blue aster -- not sure those get you privacy though.