Winter, Snow and Shoulder Season Hiking
The off-season for hiking in Japan typically spans from late October through the end of June or from late fall to late spring. During this time, the higher peaks will be covered in snow and require not only appropriate winter gear like crampons and ice axe, but also the skills to use them for self-arrest and avalanche safety.
(If you're looking for snowfree and easy winter hikes click HERE)
In the alps and higher peaks, the first snowfall is usually around the end of October. By the end of June, the majority of snow will have melted, but this also depends on the peak and year, so checking current trail conditions is necessary when hiking during the off-season.
In general hiking during this time is quite different and requires more planning, gear and experience. Huts will be closed, busses are not running and trails are different too.
This is why it's important to do proper research beforehand. A good example is "Yakedake" mentioned below. In summer only the North peak can be hiked, but in winter generally the South peak will be climbed. The winter trail up goes along the ridgeline because the summer trail has a high avalanche risk. Make sure you know the trail beforehand and don't rely on just "following" somebody elses tracks. The weather changes quickly, it might start snowing and within 10min you have no visibility and tracks left.
Lastly, keep in mind that the gear needed for hiking in snow and winter differs from summer hiking. You'll not only need warmer clothes but also special gear like crampons and ice axe, as well as emergency gear like bivy and sleeping bag. Weather changes are common, and you need to be prepared to be stuck on a mountain if that happens and survive the night.
Also, make sure your rescue insurance covers mountaineering, as many insurance policies exclude hikes that use crampons and an axe.
General Warning: I would not recommend doing any peaks or winter hikes without an experienced friend. Mountains in winter are not forgiving if you make a mistake. If you don't have any experience, take a course first.