Welcome to a land without central heating and no insulation, because that's what Japan is! Get used to being able to see your breath in your living room during winter. Don't worry about your refrigerator being tiny because your entire apartment is a refrigerator now!
Now, make no mistake, I like winter a lot. I don't like winter inside my living room, though. Where I live in the US gets pretty cold; even without wind chill we get below freezing easily. Our Halloween costumes are made to fit over snowsuits. We don't have snow days because if we got days off every time it snowed a lot then we wouldn't have school between November and March. Compared to that weather Japan should be easy. It barely gets below freezing here on the island and it rarely snows. Then again, thanks to the complete lack of insulation in the average Japanese building even low temperatures are too much.
Japan has four major types of heating: the kotatsu (heated table), the space heater, the kerosene heater, and air conditioner being a heater. Each has good points and bad points.
The kotatsu is my favorite. It's about the size of a coffee table, and it has a small space heater in it. You put a blanket, or kotatsu futon, over it, turn it on, and roast your legs. It's the most economical in that most of the heat stays under the heavy blanket. The drawback is that it only really heats your lower half and tricks everything from the waist up into thinking it's being warmed. This means that if you fall asleep under your kotatsu you'll get the mother of all colds. Don't fall asleep under your kotatsu!
Next up is the space heater. Expensive to run, but very powerful. They aren't as economical as kotatsu since the heat is all escaping into the open air, but they're indispensable for when you can't type because your fingers have frozen.
The kerosene heater is the standby of every school and many ALTs. They terrify me. If you don't keep a window open then the fumes will kill you. It's like Darwin's heating device!
Last is the air conditioner acting as a heater. This is a good way to heat an entire room instead of just a certain part of the room. Some people say that it's more economically sound to fill a barrel with 1000 yen notes and burn that in the center of your room. Very safe, but expensive.