In Japan, especially Hokkaido, it is often possible to camp anywhere. In summer, it is not uncommon to see tents pitched right outside stations, even in the city! So if you like and are well-prepared for snow camping, Hokkaido is heaven. The number of hotsprings make winter camping a great way to explore Hokkaido on a budget. That way, you can spend your hard-earned cash exploring the variety of mountains and snowboarding options.
If you like snow camping, basically find yourself a nice, quiet spot, as asking "Where can I camp?" will only end in looks of disbelief from the locals. At Kurodake, I've camped in the car park and behind a nearby shrine, but anywhere you like is fine. In summer, there is a facilitated campsite just before entering the Sounkyo area from Asahikawa.