I would personally give it a miss, especially considering the expense of getting there. The best times to ride in Japan are in Autumn or Spring. Mountain roads can be snowed-in until early summer. We helped this guy across this snowfall on a road in the Japanese alps, but we decided to head back as our street bikes would have slipped down the gorge, possibly making us inconveniencing and embarrassing the rental shop owners. Winter in Japan runs from about November to the end of March.
Snow falls in the mountains and on the Japan-sea side.
Definitely not riding weather, although daytime highs are almost always above zero. April can also be quite cold, but May is usually a nice time to ride. The cherry blossoms start blooming, and much of the countryside is covered in pink flowers. This season extends into June, depending on the area. Summer, as I explained, is very hot and humid, but not totally unbearable.