What's the best time of year to ski in Japan?

Depends on your needs, because "best" splits into two different answers.

If deep snow is the point, aim for the second half of January through the first half of February. That stretch reliably has a full base built up with fresh snow landing on top, without yet drifting into the wetter swings that can turn up by March. Go earlier, especially in the first half of December, and you're gambling on whether enough has fallen to open the trees; go later, into April, and only Hokkaido or a genuinely high resort like Okushiga Kogen is still a safe bet.

If you're chasing sunshine, easier skiing, or travelling with people who don't care about powder, go later in the season instead. March gives you long light, softer groomed pistes, and fewer people fighting for a restaurant table, at the cost of afternoon snow that can turn heavy.

Two calendar traps matter more than the month itself. New Year is generally the bigger squeeze in Japan, though Christmas week itself is also busy, specifically at the big westernised resorts like Niseko and Hakuba. Chinese New Year used to be the other one to dodge, but it isn't the automatic red flag it once was: Chinese visitor numbers to Japan have dropped noticeably amid the ongoing diplomatic dispute between the two governments. Check who actually visits your chosen resort before assuming anything; Australian school holidays now matter more at plenty of places than the Lunar New Year dates do.