How do we get there?
Chuo taxi- offer a door to door, anytime service at reasonable rates about 14000yen per adult (less for kids). The journey takes 5-6 hours. This is a great option for a family or group or if you have limited time & want to be on the slopes as quick as possible.
Nagano Bus Shuttle is a 5-6 hour journey leaving from Narita Terminal 2, costing around 10 300 yen per adult (less for kids).
Train- JR Line from Narita you can catch an express train (60-90min) from the airport into Tokyo Station. From there (depending on what time you arrive) it's the Horuriku Shinkansen (bullet train) to Iiyama. The cost is around 8700 yen and half price for kids. At Iiyama you can catch the Nozawa Onsen Liner for 600yen (they are just outside the terminal. Obvious and leave regularly) and you'll be there in 20 minutes. Alternatively you can catch a taxi and the journey will take 15 minutes.
Another option is to catch the Keisei Skyliner into Ueno and get on the shinkansen from Ueno to IIyama.
The only people you ever see struggling with luggage on trains in Japan is foreigners! When the Japanese travel they use a courier
service to send their luggage on beforehand. The trains are not designed to store large amounts of luggage so it can be a real pain
particularly if your travelling with kids. The luggage service is fast, efficient, reasonably priced and allows you to travel light. This is
particular great if you have a few days in Tokyo at the beginning of your stay. Yamato Transport are located in Narita Terminal 2
(look for the black cat logo) or there are depots dotted everywhere in the cities and towns.
If you need to stay overnight in Tokyo there are endless options in and near the airport and in the city. A bit of fun, low stress and very inexpensive is the Nine Hours Capsule Hotel in Terminal 2 at Narita..