Road to Takachiho in January

We are considering driving to Takachiho, from Kumamoto in early January next year, rather than taking the bus from Nobeoka or Kumamoto

Is that road likely to be snowed under? Would the car need winter chains? Or would snow tires be sufficient? We would drive in the day time only, after 9am and before 5pm. We have driven in winter in Shikoku before with snow tires.

I understand that Takachiho gorge is down a steep road so we would probably walk there from the town, rather than drive there if there is ice on the roads.

We have been to the gorge before in late November and wanted to revisit the place and spend more time. However, we only have vacation time after Christmas and during the first 10 days in January.