Are they A. konjac Anna? If so cold up to a hard frost knocks them down is OK as long as they're dry. Cold and wet can lead to rot so a really well draining soil is important this time of year. I'll be lifting mine (in ground) in a couple of weeks, before frost, and just cutting off the leaf.
This one flowered in the Spring but took forever to leaf out so the tuber will probably be small.
August 26 and today.