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Butterfly bushes will take severe pruning. Some people even cut them back to the ground yearly. The next time you prune, simply prune it to the height and shape you would like. It can handle this with no problem. This article may also help: https://www.gardeningknowhow.com/ornamental/shrubs/butterfly-bush/butterfly-bush-pruning-how-to-prune-a-butterfly-bush.htm

Here is an article or two that you may find helpful: https://www.gardeningknowhow.com/ornamental/shrubs/butterfly-bush/propagating-butterfly-bush.htm
https://www.gardeningknowhow.com/ornamental/trees/tgen/how-to-root-cuttings-from-various-shrubs-bushes-and-trees.htm

This article will help you:
https://www.gardeningknowhow.com/ornamental/shrubs/butterfly-bush/butterfly-bush-pruning-how-to-prune-a-butterfly-bush.htm

I would wait until spring, just in case of further snow. The damaged limbs will actually protect the rest of the plant in the snow.

Nothing bad happens if you do not prune them. They just get bigger, really. Many people prune to keep them smaller and in a more "formal" shape, but if you do not prune, they simply get bigger and have a more wild shape.

You know, sometimes butterfly bushes just take a bit longer to come up after a hard winter. It should be able to take the cold and may just be taking its sweet time coming up.

You can check the roots if you want, to see if they are still pliable and alive, but I would give it at least another month before writing it off.