Hokkaido is one of Japan's best places for camping, but beware of the nighttime chill - even in the summer months you'll need a good sleeping bag. In particular, the southwest coast can be surprisingly cold, due to the ocean currents.
Many of Hokkaido's cheaper accommodations slap on an extra fee for winter heating å¬æææ¿ tÅki danbÅ, as Japanese houses even in the north are notoriously poorly insulated and chew up vast quantities of fuel when the temperatures fall. This shouldn't be more than ¥500 or so.
If you are coming for the mountains, be sure to stay in one of the many mountain huts å±±å°å± yamagoya in Hokkaido. Most are free, and they're both a cheap sleep and a good cultural experience. You'll be sure to make Japanese friends as well.