Answer: Butterfly bushes are deciduous shrubs, losing most or all of their foliage each winter. In a very cold winter they may die back to the ground or close to it, but will remain alive at the roots and regrow quickly the following season.
Their typical natural shape is a bit unkempt and they bloom on new growth of the season, so most gardeners trim them back quite hard each spring to encourage bushy new growth. The annual pruning would at a minimum consist of removing any winter killed branches.
These shrubs are quite popular in the perennial garden because they bloom during the heat of summer and also attract many butterflies. They also add some structure or visual interest to a perennial garden during the winter by virtue of their height.
I hope this gives you some idea what to expect.
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