Do grapes need a frost to ripen?

Absolutely not. There are early and late season varieties, an early season grape left on the vine until frost will be mushy and overripe.
Once a frost hits the vine and all the leaves are burned off, any further photosynthesis or ripening will cease. Due to the high sugar level in the grape it may not be damaged by the frost but will soon start to decay, just like any other fruit not refrigerated.