“NOTE: Mountain Bikes are not allowed on Fuji during July and August hiking season”
So before or after that it should be OK, and the guy in the link did it seeming w/o any problems.
Hey,
Yes, I am riding after the oficial climbing season when everything on the mountain is closed. I did talk to the officers at the saftey hut at the 6th station and they said it is ok to bike down after the climbing season. I am not riding up. Even the most skiled of riders would not be able to negatiate all of the obstacles on the route up. The route down is mostly loose terain composed of sand/small lava rocks. The ride will involve alot of hop/slide. I’m am looking forward to it!
-mike
helmet, gloves and leg protection - You can’t be killed! 
Please don’t listen to me!
Definitely let me know how this all goes. I recently moved to Japan and have unicycling down Mt. Fuji on my to-do list for the few years I plan on living here.