I once spent a weekend in Nanto, a very short stay considering it took about a half-day to get there and back. Buses arrive every ninety minutes during peak hours, so make sure to plan well and be prompt if you visit.
I spent one night in Ainokura (相倉), one of a few old villages with Gassho-style (合掌造) thatch rooftops, in a minshuku (民宿): a family-operated bed-and-breakfast inn. When I got off the bus, the air was frigid and the skies were dark. Finding the house was a mystery I don't remember how I solved. I was the only non-Japanese native staying at the inn, but felt so welcomed. I had a wonderful time and violently urge you to do the same.
The village itself was beautiful. I awoke before dawn and took a stroll among the houses. The fog had yet to lift, but I packed my things and got onto the bus to Shirakawa (白川), likely the most famous of the Gassho-style villages in Gifu prefecture.
96% of Shirakawa is covered in forest, and it is one of the snowiest places in all of Japan. You may have seen it in photos, its white, snow-covered straw rooftops emerging from the snow-covered landscape. A perfect, wintry, Japanese wonderland.