And that's a good thing. The formation of ice crystals within and around a cell can destroy it.
But the best part? The crunchy, sweet taste of a post-frost carrot. Relish their survival skills, rendered futile by your ability to yank them out of the ground (or, you know, buy them at the store.)
This post-freeze deliciousness will be true of any of the vegetables that can survive a hard frost. But in potatoes it can cause an unpleasant side-effect. Because of the sugar content in a frosted potato, cooking can actually cause carmelization and turn your spuds brown. You can avoid discolored dishes by letting the potatoes sit in a warm place for awhile before you cook them.