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According to Snow Japan,
For most resorts, the ski and snowboard season in Japan generally starts around mid-December and goes through until around early April. Opening of course depends on the level of snow that accumulates at a particular resort, and some resorts do actually open as early as late October ("early skiing") and can continue to operate until mid-May (for "spring skiing"), usually with the help of snowmaking machines.
They list 88 resorts in Nagano so you could use that as a starting point to find resort web sites for more details and predictions about this year. I know that Canadian resorts will have a planned opening date on their website before they are actually open.