Why not? OP surely knows that he's going from a warm season in the southern hemisphere to a cold one in the north. But Tokyo doesn't get terribly cold in the winter, and it's usually very dry. Skies are often cloudless. A typical January day in Tokyo is crisp and pleasant - Much nicer than, say, London IMHO.

As for hotel choice - Given the arrival at HND, The Strings is worth considering. It's easily the most accessible location from HND. As the OP noted, it's not in an interesting area, but it's easy to jump on a train from there to most other parts of town.

Another option that I'd look at is the hotels near Shinagawa / Shiodome - I'm thinking of places like Conrad (de-luxe), Royal Park Shiodome Tower (4*?), Shiodome Park Hotel (4*?), Mitsui Garden Ginza Premier, Courtyard Ginza Premier Hotel (Marriott chain), Villa Fontaine (Business hotel) etc.
I find that the cost performance is pretty good. Access from HND is good (Take the monorail to Hamamatsucho and then a cab). Onward access to Nozawa Onsen via Tokyo Station is easy (take a cab or the Yamanote line to Tokyo station).