An alternative to taking the trains from Tokyo is to use the Nagano Snow Shuttle which goes from both Haneda and Narita Airports and goes to Myoko Kogen. This shuttle also collects guests from Nagano station.
This is the a link to the timetables for the snow shuttle
Narita Airport -> Myoko Kogen http://naganosnowshuttle.com/myonrt.aspx
Haneda Airport -> Myoko Kogen http://naganosnowshuttle.com/myohnd.aspx
This is another shuttle that operates from Narita and Haneda airports to Akakura.
Here is a link to more information: http://www.chuotaxi.co.jp/publics/index/10/
Another option is to take the new ski shuttle from the new Joetsu-Myoko Shinkansen (Bullet Train) Station. This shuttle is a free service that runs between Joetsu-Myoko station and Akakura.
This shuttle operates daily between 26th December and 8th January and operates on Saturdays, Sundays and Public Holidays from the 9th January to 21st March.
The details of this ski shuttle are available at this link: http://www.myoko.tv/news/3997.html