The answer is affirmative all the way. It operates EVERYDAY.
Here is the timetable:
http://www.hakubagoryu.com/access/jr/tyojr1.html
In case your Japanese isn't great, here's a summary for you. (Super Azusa only)
Shinjuku ---> Hakuba
Between 8:00 and 18:00, the Super Azusa will leave Shinjuku once every two hours. (8;00, 10:00, 12:00, etc.)
Hakuba ---> Shinjuku
6:09
8:53
12:23
15:43
16:28
17:58
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On the average, it's about a 4-and-a-half-hour ride one way.