Cheap way to travel from Kyoto to Nagano

We are a family of 4 (2 kids aged 12 and 13). We plan to go skiing in Nozawa onsen (Jan6-10, 2014). Before that, we will visit Kyoto and Nagano (just to take a bus to Snow Monkey). What is the cheap way to travel from Kyoto to Nagano station on Sun Jan 5, 2014? It seems to be a busy period that people travelling back to work. If we need to take a train/bus, do we need to reserve the seats in advance and how?
Thank you,
Muk

http://www.japan-guide.com/e/e6003.html

Thank for the website. If we would like to take a train (LTD EXP Shinano 9) leaving Kyoto to Nagano at 9:25am on Jan 5, and we can only reserve the seats when we arrive Japan on Dec 26 at night, would it be in time? We need to book and pay for all the accommodation in advance and don't want to find out that we cannot get the train to go there. Thank you.

There should be a few more like this, but this is one of your options if you want leave Kyoto at night and arrive in Nagano station or Yudanaka in the following morning for 6,000 yer per person. You save money one night for your accomodation.

Now, you need to make reservations. They start taking the reservation 30 days in advance. So if your day is Jan 5th, you can do it on Dec 5th. You ask your hotel in Kyoto to do that. You buy the tickets upon the deperture.

It looks like the highway express bus runs (every night) through to Yudanaka, final destination (Sonow Monkey place) after making several stops including Nagano station.

http://www.nagadenbus.co.jp/highway_ex_index.html

The bus comes from Osaka and stop at Shin-Miyako Hotel in front of Kyoto sation. So the best place you stay one night before might be Shin Miyako.

It's written all in Japanese. So you will need an assistance of your hotel. Many foreign tourists love the snow monkeys.

Thank you, Jay Kay, for a better and cheaper option on a bus. Could you recommend a website for a day bus as well?

If we can rent a car cheaper, would you recommend to drive on Sun Jan5 (rent from Kyoto and return in Nagano)? Would the traffic on the road be very bad? If we can change a schedule to drive on Mon Jan6, would the traffic be better?
Thank you for your help.
Muk