It all depends on the type of soil you have and how deep the dahlias are buried. If they are deep down and you have light soil (doesn't get soggy) you probably could leave them where they are (you could always put a layer of leaves or ferns over the top as insulation). However, if this is not the case you need to pull them up take the greenery away (often best to do this after two frosts) and store them in a dry cool dark place. My father used to store his in a box in the attic.
One important point not yet mentiioned is, if you intend to dig them up, take as much soil off them and turn them upside down so that they `drain` off any moisture within them, and leave for several days before storing in fresh nearly dry multipurpose compost in a cool greenhouse, or shed away from frost.