Walk Magome to Tsumago in early Dec

My young family and I wish to visit the Kiso Valley and to do the 8km walk between the towns. Is this safe to do in Decemeber? I have heard the restaurants and shops close during the Dec to Feb period. Is this true? We plan to stay in Magome for 2 nights, do the walk down and return to Magome by bus. Is this possible?

Is this safe to do in Decemeber?

It depends on the weather. But unless it is not during a major storm or immediately after a major snow storm, it is going to be safe. I don't think that the area usually sees snow in early December. Check the weather. And maybe consult the hotel staff and tourist information office if you are in doubt.

I have heard the restaurants and shops close during the Dec to Feb period. Is this true?

There are no restaurants and shops along the walking route! As for the restaurants and shops in Magome and Tsumago, my understanding is that they are open around the year.

We plan to stay in Magome for 2 nights, do the walk down and return to Magome by bus. Is this possible?

Yes. Here is the bus timetable:
http://www.japan-guide.com/bus/kiso.html