welcome to the forum!!
well, even tho it did freeze in your area - totally unusual - i'm sure it wasn't cold long enough for the ground to freeze up, so the roots are probably okay. especially if this is a well-established plant
so, trimming back the damaged parts would be the thing to do. trim back a bit and look at the cut end...keep trimming back (every 6-8 inches or so) until you see healthy green inside.
cutting back to ground-level would probably be okay too...i'd hate to see you lose so much of your vine tho - especially if it's not really needed to give it such a drastic trimming!