Hi Dianne,
Children below the age of 6 travel for free, so that's good news to start with :)
I've made a list of normal ticket prices to see if any JR Pass would be economic.
Narita Airport - Tokyo ¥ 2,940
Tokyo (Shinjuku) - Hakuba ¥ 8,070
Hakuba - Kyoto ¥ 12,700
Kyoto - Tokyo ¥ 13,220
Tokyo - Narita Airport ¥ 2,940
For a total of ¥ 39,870. A 7 day JR Pass (¥ 28,300) could be helpful here if you could do at most of the travel with it.
A possible option would be to take the train to Tokyo on the day of your arrival and stay the night there before and travel on the next morning to Hakuba and start using your JR Pass at the same time. This way you could cover most of your travel with the JR Pass and also take advantage of the Azusa Express which leaves Shinjuku (Tokyo) every morning at 7:30 and is the only direct express train between Tokyo and Hakuba on a single day.
This way you can cover all of your long distance travel with the JR Pass and you would only have to buy additional tickets for the return Tokyo - Narita Airport.
Otherwise I would suggest going for normal tickets, as there's no other pass except the JR Pass which covers all your travel.
Enjoy the snow!
Daniel