Depending on your budget and arrival times, taking the bus maybe a good option for you as an alternative to the Train or Chuo Taxi. For example, if you arrive after 5pm taking the train to Nagano, you'll more than likely miss the last local bus service to Hakuba, requiring you to stay over night in Nagano.

Hakubus
Narita to Hakuba.  Tues/ Wed (waits for Jetstar flight 25), Departs: 9pm - Arrives: 2am. Rest of week, Departs: 8pm - Arrives: 1am. 
Hakuba to Narita. Departs: 11am - Arrives 5pm (via Tokyo)
Price: YN9,700 on way, YN17,640 return.
For more information and to make a booking visit www.hakubus.com