Some Canna are more hardy than others, as are some Ginger. I don't cover/mulch my Canna or Ginger at all, and we get down into the lower teens (infrequently) and mid to lower 20's (frequently). I would mulch with 6-12" of leaves, pine straw, or similar if we got into the single digits. Below 0F, I would dig it up.
Unfortunately my only experience in growing those plants is here in NE Mississippi. We never get snow, or least very seldom do, and it generally won't last more than a day. My understanding is that snow is a great insulator in areas that get really, really cold and insulates again the affects of wind chill as well. You in the midwest, north, northeast, and mountain regions know way more about that than I.
