Possible to do Kumano Kodo early December?

I am considering doing a multi-day hike the Nakahechi trail on the Kumano Kodo this year during the first full week of December. The one concern is temperature - is the weather typically too cold or too wet during that time of the year on the trail to safely do the distances?

We are experienced hikers and have looked at the Kumano Travel website to plan out our route. We are normally comfortable with hiking temp with a high around 15C.

The question is what is the lowest temperature you are comfortable hiking. You wrote your highest temperature is 15 C. It will be colder than that.