Mongolian warriors of old were said to have used their helmets for cooking their food. Jingisukan (Genghis Khan) BBQs today are typified by a helmet shaped hotplate BBQ on which slices of mutton are grilled. People gather at the BBQ swapping stories, jokes & Arkhi (or sake) much like the Mongol warriors during breaks from conquering and warring. Although, it may not have its origins in Hokkaido, the BBQ is popular here as it's warming qualities are well suited to the region's icy winters.
There are lots of good restaurants in the major cities where they tend to be located near the red light districts. Maybe it has to do with the supposed libido enhancing properties of grilled lamb. You may find a couple at Hokkaido ski resorts and ski villages. Seek them out as an after ski session with your crew grilling up hot sizzling meat and downing icy Sapporo Classics is a memorable part of any snow trip.