Basically, both the common boxwood (Buxus sempervirens) and the small-leaved or Japanese boxwood (Buxus microphylla) are sufficiently hardy for local weather conditions and do not require additional winter protection - at least as long as they are planted out in the garden. A box tree in a pot, on the other hand, is dependent on insulation that is effective against frost.
A box tree in a pot should be packed up well for the winter
Boxwood in a pot needs winter protection
The reason for this lies in the small amount of soil that encloses the roots of the boxwood in the pot and cannot protect them from freezing. The substrate layer is too thin for this, which is why you have to help out in winter with insulating material, such as garden fleece. Wrap the pot with it and also place the planter on a thick piece of wood or polystyrene. In addition, it makes sense to move the plant directly against a house wall and, at best, to place it in partial shade - sun plus frost often leads to frost damage.
tips
The boxwood also needs water in winter, so don't forget to water it!