>>644401I did Mt. Fuji in the summer on the Subashiri route.
What you need will depend a lot on the actual conditions you happen to get when you are there. Winter climbing anywhere in the world can be highly unpredictable.
At the very least I would bring climbing snowshoes (like MSR Lightning) and trekking poles. Crampons and ice axe would be prudent because you don't know what the conditions will be like for ice or steepness on your chosen route and they will likely be valuable nearer to the top. On the Subashiri route I would say some portions were steep enough that crampons and axe would be appropriate.
You should also be aware of avalanche risk, since basically the entire mountain is perfect conditions for creating big avalanches above treeline.
Personally I would be impressed if you can do Fuji in winter in 12 hours or less. Even in the summer hiking times are typically 7 to 11 hours round trip. I think the smartest choice would be to rest around the treeline, and then start up at about 12pm-2am. Generally you want to be up and down before the avalanche risk is too high during the day. Of course keep in mind that if it snows and you lose your footprints, you might have a hard time finding your way back.
Have fun!