Yes they do. I had carrots when I lived in Spencer and picked them with snow on the ground. I had cherry tomato plants that i let grow all along the ground and in the beginning of winter the plants would be close to 25 foot long. I gathered one plant up into a circle and covered with leaf litter thinking in the spring I will burn it. It had a lot of green tomatoes on it in the winter but i was done picking. Spring rolls around and I decide to stir the leaf litter up and I discovered a bunch of red tomatoes still attached to the vine. They Were very tasty! Vine was still rooted in the ground.