When temperatures drop and frost hits, only the heartiest of veggies are equipped to survive. And for many of them, the adaptation that keeps them from dying in the cold also makes them sweet and delicious.
In the above video, UCLAbiochemist Liz Roth-Johnson explains how this works for the crunchy carrot: When it gets cold out, carrots (and parsnips) convert some of their starch stores into sugar. They do this to keep the water in their cells from freezing, and it works in the same way that putting salt on a road keeps it from freezing over. When a foreign substance mixes with cold water, it makes it harder for enough water molecules to reach the surface and freeze there -- so the freezing point gets lower. The cells inside a carrot might have icy-cold water, but that water won't turn into ice.
And that's a good thing. The formation of ice crystals within and around a cell can destroy it.
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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 carmelizationand turn your spuds brown. You can avoid discolored dishes by letting the potatoes sit in a warm place for awhile before you cook them.