Jigokudani Snow Monkey Park I visit half a dozen times per year, I recommend two lenses 1st a 24-105mm, 2nd a longish zoom lens reaching 300mm-400mm. The 24-105mm I have found most useful since we can get within inches of the snow monkeys, the photo on this blog taken at 100mm. A Telephoto is ideal for action shots, especially when the youngsters who by nature get restless sitting, quickly jumping out of the hot springs, they do enjoy playing with friends in the snow.
If you have questions about other gear needed by season, or anything else about photography travel in Japan, please feel free to contact me.

Happy Monkey Photography