Sweetening

This is due, in part, to these plants ability to convert starch into sugar. Over the course of the growing season, vegetables store up energy in the form of starches. When temperatures start to drop, they convert these starches into sugars, which act as an anti-freezing agent for their cells. 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. 

But the best part? We get to enjoy the crunchy, sweet taste of a post-frost carrot.