In October, you can enjoy Koyo (autumn leaves) in Nyuto Onsenkyo. Great to hike upon the Mt. Komagatake, also nice to walk in the beech tree forest around Taenoyu too.
Koyo season starts depends on the weather and temperature.
This is Tazawako Tourism Association’s website which shows the progress of Koyo. Check 乳頭温泉郷, it shows by colors Green to Red.