Are there fixed dates for the openings of ski resorts at Nagano or does that depend on the snow fall?
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.