I grew these Danvers Half-Long Carrots in the 2011 season and saved the biggest and best by breaking the tops off and burying them in very loose soil in the same manner that they would have grown in the first place. They were all at least 3 inches below ground level and these have been in the garden for a few months. I put them into the ground where my potato patch was because that soil was already well worked from the massive potato crop.
This was my first attempt at this trenching method for keeping root crops and I was quite happy with the results. Make sure you mark the location well so you don't end up finding them with the tiller next growing season. Needless to say I will be using this technique in the future on carrots and other hardy root crops. The only problem you may have to deal with is an animal who likes carrots as much as you do taking some for their own winter snack.