Hi Garden_Whisperer,
Go to the garden ( if you have one) with a shovel make a 50 cm*50 cm*50 cm hole - well a one meter depth would be better but ...
Put the cuttings inside, and put some wood frame over the hole. Put some straw/plastic cover over that, if you have, and you should be done .
Here, some do conserve their carrots like that during the winter.