A. Buddleia is marginally hardy to zone 5.While it is evergreen in warmer climates, it dies to the ground in most of Canada where temperatures go below 20°F degrees (-7°C). Be sure it is dead and not just dormant before digging it up.
It has a better chance of surviving our weather with a good layer of winter mulch; however, wait until the first hard frost before putting down the extra mulch.
There is another species, B. alternifolia, that is reportedly more cold hardy than B. davidii. You might give that species a try.
Lake Simcoe South Master Gardeners