Cut off the broken, leave the rest until after bud break in spring. Same as with roses, the concept at work is that stem die-back due to cold starts at the end of the stem, so if you shorten the stems markedly before winter they may die back farther than they would if the stems were longer during the cold period.

Most woody nursery stock I see here has deformed roots due to failure to pot it on in a timely manner at production facilities. Fast-growing items like butterfly bush are all the more likely to be disadvantaged by bound-up roots at planting time. Yours may have gone over due to this problem, unless their bases are still upright, with some branches broken off above this point. If they did pivot over on knotted roots, you are never going to be rid of this vulnerability without digging them up and correcting the roots, or starting over with smaller replacement specimens that have their roots corrected at planting time.

Cuttin back Buddleias in fall, even in zone 6, often results in their death. I would wait until early spring.

in my experience .... in MI .... they are extremely short lived in z5 ... so no matter what you do.. they may die ...

just so you know... so if they die.. it most likely will not be related to whether or not you prune them ... again.. in my experience ...

ken

Thanks for your input. I decided to tie them up and prune them in the Spring.

I cut them to within a foot from the ground, each Winter. No problem. But it could be done in Spring.