As long as the old stems (canes) are alive they will send out new growth. A hard freeze will kill back mature stems but a frost will only kill back soft new growth. I'd prune away dead stems after a hard freeze but would just leave them be after a frost. The dead tips will usually just dry up and drop on their own. If there's more living plant when the temps warm up it's likely that you'll get blooms sooner.

I would wait a week or two before pruning away the bigger trunks/stems.Sometimes they look fine initially but later you will find the outer bark loosens and slips from the wood. This means those stems are toast.

I leave everything alone till spring. Pruning will sometimes stimulate new growth, especially during warm periods.
Tally HO!

Thank you all for the good advice! They are certainly not very attractive in their present state but I will just wait for spring to do any pruning. I have always wanted more of a tree shape but wasn't sure how or when to prune. Now that I know how tough these guys are I think I will try a little creative pruning in the spring.

As everyone has already mentioned, they resprout as long as the canes are alive. Mine always lose branches in the winter, but the main canes (or trunks)remain alive. The trunks on mine are over 6 feet tall.

Surprisingly, I have a customer from Indianapolis who planted her brug directly in the ground with her musa basjoo banana. Now I recommend on the basjoo here in zone 5 to mulch them with bags of leaves piled up on top of the banana plant in the winter. She did that with her brug too and it came back from the roots. Those are sure tough little buggers!