It has a chance in USDA zone 6 with mulching and is OK in zone 7 and higher. Potting up will work, but you need to get fine roots and stolons (runners) as well as the tubers. Digging up means root pruning, so a lot of the tops also have to go, but you should leave some foliage to provide energy and tissue for new roots and leaves.

Are you in USDA zone 5? If so, cold frames and unheated sun rooms/vestibules/porches/greenhouses can be very useful. Keep the plants from freezing solid and keep the soil damp, not wet or bone dry.

I have kept Black and Blues going for 3 years now in pots inside over the winter here in western NY but this year I am just rooting cuttings to overwinter inside as it really got to be a problem with so many plants and not enough light sources nor room to put them all. I took cuttings two weeks ago of my main Black and blue plant that are in the ground and they have already rooted. They are just way too big (thank you Rich) and still way to loaded with blooms to dig up. I will be heavily mulching them for the winter and then when it warms up in the spring I will cut them back and see what happens. I have some zone 7 plants that survive and I have lost some hardy zone 4-6 plants in past years so it depends on where they are planted and what kind of winter you get this year.

Penny