It'll die back to the ground but resprout in the spring (possible early summer). Crape myrtles don't begin to leaf out until temperatures at night are in the upper 60s and 70s. The question is, will the tree have time to grow back to where its significant enough to take the time for before the next frost kills it to the ground again? I'd recommend growing one in a large pot and brining it in during winter. Heading off the leader so it does not grow too large to bring in.

I've heard stories of them growing in NYC, so microclimates are important. The retained heat from the city concrete allows then to survive winter.

Climate zones notwithstanding, crape myrtles don't like their feet wet. You want a tree that is adapted to that much water.

If damp Magnolia virginiana is an obvious choice, if climate and soil (it does not like alkaline) otherwise suitable.