We, family of 5, are planning to visit Japan Tokyo towards the last week of January 2017. My kid...

Hakuba Goryu Tourism Association in Nagano Prefecture is carrying out 'Muslim friendly project' since 2011. 20 lodges among 80 seem to serve Halal food and use Qibla seal in their guest rooms.
The Hakuba valley is world famous for powder snow and previous winter Olympic venues. I live in Matsumoto near Hakuba and have enjoyed skiing in Hakuba Goryu & 47 Snow Resorts many times.
There are direct bus services from Tokyo to Hakuba.
See http://www.hakubatourism.jp/skimap/hakubagoryuhakuba47/ for the information of Hakuba Goryu & 47 Snow resorts.
Enjoy the Japanese snow.

The closest ski resort from Tokyo that cater to Muslim's needs is the APPI Resort in Iwate. It can be accessed by Shinkansen from Tokyo Station to Morioka Station (2h 13m) and from Morioka Station there are shuttle buses to the restort that can be used free of charge by hotel guests.
See this article for more info:
http://www.halalmedia.jp/archives/9259/appi-ski-resort-iwate-prefecture7-services-muslim-customers/

Although getting Halal food may be difficult, I can personally recommend Nozawa Onsen(Nagano) and Kusatsu Onsen(Gunma) as great places for skiing and onsen (Japanese hotsprings) closer to Tokyo. The snow conditions are great in the this area and if you are looking for powder snow near Tokyo look no further. Especially Kusatsu Onsen has a lot more to offer than just skiing as it is one of the most popular places to visit to enjoy Japanese hotspring and its culture.
The hot springs are generally large public baths shared by a large number of people. Although private baths can sometimes be provided and you could check if private baths are available with the hotel or inn beforehand.

Other Halal ski resorts that cater to Muslim's needs:
Rusutsu Resort in Hokkaido
Sahoro Resort in Hokkaido

I hope this can help and if you have any more questions please feel free to ask them.
Have a great trip!