For the most part, the grower waits and watches. Six hours after the temperature returns to above 60 degrees F, a cut can be made into the active bark and wood to see if there is any damage. If the bark is brown, the vine is dead. Check about a foot above the ground on the south or southwest side of the vine where the sun contacts the trunk, this is the most common point of damage. It is possible for the shaded north side of the trunk to be damage free, so check it also.
Live bark is white, freeze damaged bark is brown.
It is also good to cut through buds to see if they have frozen. If the freeze is marginal, it is possible to kill buds without killing the trunk. The further north you go in Texas, the less freeze damage you will find because the vines have been receiving very cool nights which pushes the sap into the roots. There are steps one can take in preparing for freeze injury. A two trunk vine is a good tool in reducing freeze injury.