Your tree did not ready itself for winter properly. It may be because its genetics is from a northern provenance (like Michigan) or perhaps you just had an unusual fall that did not trigger the internal winter changes in the tree early enough. The fact that the leaves are yellow, and did not freeze green is a good sign. It's likely there will be no consequential damage, although only time will tell.
You say the tree is young. Some juvenile trees tend to hold leaves much longer into the fall/winter than what is "normal" for an older tree. Usually this trait lasts for only a few years. I am not sure if Redbud exhibits this phenomenon or not.
