My two-week trip started with a group trek along the Nakasendo Way, led by Walk Japan. I stayed at an assortment of centuries-old ryokans (historic Japanese inns) and ate traditional foods.

In true British fashion, I’d always turned my nose up at the idea of a holiday that didn’t involve heat. The UK summer is unreliable at best, and if it wasn’t sun, sea and sangria, really, I ...