Mt Fuji is only open for trekking in July and August only!By November, it will be frozen with snow.
Off season climbing Mt. Fuji is not impossible but is not a simple hiking any more. Winter climbing is a mountaineering requiring equipment and skills. Definitely, November is almost impossible but late September and after late March may be OK.
http://www.geocities.co.jp/Outdoors-River/3531/FjiadGnr.html
Guided tours during off season are available.
http://www.fujiyamaguides.com/english/tours/index.html
Do any ching know any accommodation still available? I registered but cannot find the accommodation. May need to give up if no place to live on 24 nov.