We just got back from Japan/S Korea on Monday and the weather in both Tokyo and Seoul was fine, although DS says Seoul will get much colder in the coming weeks.
Right after we arrived into Haneda, DH and I travelled out to Yamanochi for a couple of nights' onsen and the snow monkeys. We delayed our plan to visit on our middle day as snow was forecast overnight on our second night and we opted to visit the snow monleys on our last morning before travelling back to Tokyo. It was a good call as snow was on the ground, and continued to fall, during our visit. We also opted to take the 8.30am shuttle from the ryokan so we were some of the first to arrive too, so I think we had the best experience we could have had.
Our thoughts were that it looked much better under snow (having seen other photos) and the monkeys were obligingly in the (man-made) onsen pool. We arrived as they were being fed, and although they are wild they obviously appreciate the food, as they swarmed in for breakfast. On the plus side the food was well distributed and they were no obvious fights, but if you watched there were clear leaders who had the best calls on the food (but I guess this is natural...). There is absolutely nothing to stop the monkeys from coming and going, and as they took absolutely no notice of the tourists I am sure they are not fed by visitors which is great. However, I worry that the 'instagram visitors' will not be as compliant with this clear instruction as the Japanese tourists have been... I am glad I went but I am also mindful that the experince was good purely because of the snow.
We saw Fujisan a few times, while travelling and from Tokyo too, so that was an added bonus of going in December.