Yes. You don't want the roots to freeze hard. You can dig holes and put the bags in them and fill them in. In my area (zone 7a) I was able to group bags tightly together against my house and mulch them in. You want to tops to stay cool but the roots not to freeze. I've also used an unheated garage. You don't want to bring them inside where the tops warm up enough to break dormancy.
If I were in zone 4, I'd be tempted to dig holes, set the bags in the holes, and then mulch heavily. The screening is a good call as well if you keep them outside where rodents have access.
Thanks,
Jack