You guys and gals in zone 5 are much braver in planting so early than I in zone 7. If you cut off the frozen growth, the eyes will be sending out new shoots and likely more than one. You can let them all grow, or break off the extras that emerge, leaving just one main stalk. Your choice.

Unless you have a very deep, prolonged freeze again, there should be no need to dig up tubers. They'll do they're growing thing with a bit more warmth and no further help from you.