The best time to transplant it would be in early spring before the buds break into growth. If the vine is very old the roots will probably be very deep and this could be a problem. You could also take hardwood cuttings when you prune it in the winter when the vine is dormant and propagate these for insurance or to grow more vines, Grape vines grow very vigorously, so it won't take too long for the new cuttings to establish.

If the vines have been planted more than a few years they will have put down a serious tap root reaching down to the water table. Moving a grape vine is not something I would recommend - suggest you go with taking hardwood cuttings as Myron has mentioned.