Is there public transportation in Hakuba (taxis, bus service)?
Yes, there are free shuttle buses for the resorts during ski season that cover most of the Hakuba area during the day, and at night there is a shuttle bus that services the main restaurants and hotels. There are 4 taxi services, and a city bus service. Hakuba is spread over a large valley (20k or so), and so you are better off finding lodging that provides free shuttle service (most do) and/or staying near where you wish to ski most days.