Don't think there's any trains or trams on Fujisan. There are buses to the 5th station, but I understand the schedule is seasonal. Official climbing season is July and August. I climbed it mid-September. You can read about it on Big Sushi, Little Fishes: …wordpress.com/2013/…
If you're going in winter, there's not much point getting close to Fuji. Much better to enjoy the view from a distance away. You'll get a great view of the mountain from the Shinkansen west out of Tokyo. Best views are about 50-60 minutes out of Tokyo depending on the train. Try to get a right side window seat!
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