I couldn't find that black woolly bear Griff found so I'll put this here.
The fur is called setae and it isn't there to protect them from the cold weather.  Instead it actually helps them to freeze more controllably. Caterpillars hibernate, creating a natural organic antifreeze called glycerol.  They freeze bit by bit, until everything but the interior of their cells protected by the hemolymph are frozen, and survive to -90°F.  The Arctic woolly worms live in slow motion, rather than 2 to 4 weeks before becoming moths they take at least 14 years. 



There are tons of similar caterpillars but the real woolly bear is the Isabella.
Each fuzzy, 1½ inch wooly bear becomes an Isabella Tiger Moth. After wintering it’s awakened on a warm spring day and continues to feed.  Soon it forms a cocoon and pupates for 2 weeks then an orange-yellow moth with 1 ½  to 2-inch wingspan emerges.  The wings lack distinctive markings but the abdomen is spotted with three longitudinal rows of small black dots. These moths are active at night throughout summer.
 
This myth, around since colonial times grew in popularity after Dr. Howard Curran (curator of entomology from the American Museum of Natural History) did a small study in 1948.  He went out to Bear Mountain, New York with a reporter, his colleagues, and their wives.  He counted the brown bands on 15 different specimens.  He then made a prediction for the winter.  This news story was published in the New York Herald Tribune.  It was picked up by the national press and the rest is history.
Moths have a bad rap because of a couple of them, like the Gypsy Moth, do a lot of damage.
But the Isabella/woolly bear doesn't wreak much damage in your garden..