Canas tend to need warm soil to thrive. I have found that even in my Zone8a climate the rhizomes tend to blacken and rot even with a heavy mulch in Winter to stop frost penetration. Those that have survived in the ground are slow to recover and have smaller rhizome density. I simply dig them up with soil, place in a pot in a dry frost free place and plant out in spring as I do with tender Gingers. If you want to keep them in the ground It might be worth covering them to stop any moisture penetration as well as a mulch. I'll be interested to see how you get on if you leave them in.