Those kinds of winter temps are way beyond anything I've ever been exposed to. It's just way warmer here which often causes plants to break dormancy and begin active growth too soon. Then a drop below freezing damages them. It's nearly always better if they hold off the active growth until that danger is past, but there are nearly always plants that have some damage. The redbud may be one of those that are late breaking dormancy trying to avoid that. The native trees here that are really late breaking dormancy, like the mesquite and pecans, get really damaged on the rare occasions they get caught. Others, like the various elm varieties, don't seem to be bothered by a late freeze and shake it off. The others end up with some dead growth and recovery is a lot slower. Since the redbud I have is even later than the pecans, it has never been exposed to a late freeze. That's just an indication of how late it is because here, sooner or later, most plants get caught by one. I think they are probably adaptable on the moisture level. I've seen them growing along stream banks where it probably stays relatively moist and on rocky cliffs in thin, poor soil where moisture probably didn't stick around long. They were fine in either location. Same with sun vs under story growth - they grew naturally in both situations. Mine is in hot sun and poor subsoil and it is managing. I don't give it supplemental water very often.
