I got lambasted a year or two ago for suggesting that redbuds are only reliably hardy (in zone-typical sites) up to USDA zone 6 and better sites in 5. (As opposed to the list of zones that someone, somewhere, is growing them in, under unusually favorable or lucky circumstances). Next time the subject comes up, feel free to share your experience :>
Yeah, they do that. And that's the trouble with woody plants all it takes is one particularly bad winter to undo a number of years' good work of growth.
The good thing is that at least redbuds CAN come back to some reasonable degree, as yours is trying to do. The green growth will indeed turn woody. Whether it will survive and the tree will recover long-term depends in large part on what this summer/fall/winter weather happens to be like. But unless you are really feeling axe-happy I'd give the thing another year or two to prove itself. It might end up just fine.
Prune off the dead old wood, though. Otherwise you can get fungus started that damages the still-living parts. If you are unsure where dead stops and live begins, do it incrementally, looking for green under the bark.
Good luck, have fun,
Pat