When they hibernate, their metabolism slows to the point that they are able to survive on the fat reserves and internal moisture for several months. Their body temperature drops during this point, so they need less fuel in their body to maintain it's temperature. They also build a den to insulate, so they lose heat more slowly.
I don't know if they are "asleep" the entire time (some hibernating animals do awaken occasionally to seek food), but SpunkySenior explains it. Further, most hibernating animals are in something more like a coma than normal sleep, and of course they are not expending energy that would otherwise warm them to the point of perspiring or exhaling water.
