Ok, I am officially jealous! Sounds like a great trip.
Here are some answers to your questions:
Narita airport on 12th January and are going straight from here to Nozawa Onsen though I believe we do have to go to Tokyo to change trains.
Yes, you have to change trains at Tokyo to the Nagano Shinansen.
I think it's pretty close on whether the JR Pass is worth it for our trip but I was thinking of getting a 14 day pass and then the 4 day JR Kansai pass for the end of our trip. Can you help?
Lets take a look at the costs of your legs, bearing in mind your trip is for 18 days:
- Narita airport terminal 1 > Tokyo: ¥2740, (62mins, 79km)
- Tokyo > Nagano: ¥7770, (105mins, 222km)
- Nagano > Togarinozawaonsen: ¥740, (58mins, 38km)
- Togarinozawaonsen > Nagano: ¥740, (58mins, 38km)
- Nagano > Tokyo: ¥7770, (106mins, 222km)
- Tokyo > Shibuya: ¥1000, (22mins, 14km)
- Shibuya > Tokyo: ¥190, (21mins, 14km)
- Tokyo > Nikko: ¥5230, (121mins, 150km)
- Nikko > Tokyo: ¥5230, (117mins, 150km)
- Tokyo > Kyoto: ¥13020, (165mins, 513km)
- Kyoto > Nara: ¥690, (49mins, 41km)
- Nara > Kyoto: ¥690, (46mins, 41km)
- Kyoto > Osaka: ¥540, (28mins, 42km)
- Osaka > Kansai airport: ¥2940, (57mins, 64km)
TOTAL: ¥49290 for 14 legs
Yes - looking at your itinerary the only rail pass that makes sense is the 14 day rail pass starting as soon as you land, and that's more for convenience and flexibility than any massive cost saving.
I'm not sure a 4 day Kansai pass makes sense at the end of your trip however. At ¥6000 for 4 days, you'll have to do another ¥3000 more travelling than you have listed at the end of your trip for it to be worthwhile. That said, the good thing about the Kansai Pass is that you can buy it in Japan, so you can leave this decision until you get to Kyoto Station and arrange it there.
Also I was wondering whether it is easier to travel with the JR pass rather than buying each ticket as you go or is it the same as you have to reserve seats anyway?
Personally I prefer the JR Pass experience as you don't have to fiddle with money/cards and can easily change plans if you fancy it or hear of a nice place to go while you are travelling. You can reserve seats (or not if you are in a rush at the station) with a JR Pass, but with single tickets you'll always have to remember to leave good time to buy tickets before your train.
How does my itinery sound, I am staying anywhere too long or anywhere not enough?
Sounds really good. You've got a good length of time in the snow as soon as you arrive, and the pace from there is very good.
If I could change anything I may suggest you spend another day or two in Tokyo over Osaka/Kyoto. Currently you are intending to say 2 full days in the capital (if you intend to go to Nikko) and then 6 full days in Kansai. As Osaka, Kyoto and Nara are so close, you can always hop between these for relatively little outlay if you need to spend a little more time in any of them. This is personal preference more than anything else however, and depends on what you're looking to get out of your trip.
Hope you have a great time!