Snow-playing at Nagano in December?

Hi!

I am bringing my 4 yr old son for the first time to Japan in Dec. We will be staying at Yamanouchi town to visit the snow monkeys. I have a few questions to ask here as I am totally not familiar with the area!

1. Will it be snowing ard 10 Dec?
2. I am thinking of letting my son play snow (he might be too small to ski. maybe just snow board or sled?). Is there any recommended place nearby to spend half a day?
3. We will be driving. Our next destination is back to Tokyo but don't intend to drive all the way back. Is there anywhere convenient for me to return the rental car and take a shinkansen back to Shinjuku?

Appreciate all advice pls Thank you!!

1)
Not exactly watch one week forecast.
Last winter 2015 Dec was very warm as record not enough snow.
http://www.hokurikushinkansen-navi.jp/pc/news/article.php?id=NEWS00000...
Read monkey park staff blog back to 2014,13... fr left.
http://blog.livedoor.jp/cpiblog00543/

Ski sites are no problem mostly snow machine using.
http://www.asahicom.jp/articles/images/AS20151124003243_commL.jpg
But that date some ski sites dosen't open if snow amount not enough.
Be careful weather conditions and open info both.

2)
Basically anywhere.
http://snow.gnavi.co.jp/search/list/spl_area01.php?areacdl=3
With "kids park/キッズパーク" best.
Karuizawa/軽井沢 and Hakuba/白馬 are very famous for foreigners.
http://promo.yadonet.jp/main_plan/0904nagano/images/t_map.png
Especially "Karuizawa Prince" access easiest in front of Shinkansen stn placed and opened fr earlier date usual by snow machines.
http://www.princehotels.com/en/ski/karuizawa/img/karuizawa_trail_map20...

Shiga kougen/志賀高原 area closest fr snow monkey.
http://promo.yadonet.jp/main_plan/0904nagano/area.php#t02
http://www.shigakogen.co.jp.e.aafw.hpf.transer.com/highlight/snow-slop...
But no exact open or not.

Maybe no need ski "sled" or similar items enough.
If already possible ride a kids bike "snow bike/snow scoot" exist.
(sample:)
http://toolatesports.com/top/news/2014_toolate_tateyama.jpg
http://4.bp.blogspot.com/-I5YAQuEgQ1Q/UvpMxahC8uI/AAAAAAAAAd0/aNtO1GyG...

3)
How to getting in Nagano also from where? (Tokyo or other?)
By Shinkansen fastest fr Nagano city(also Karuizawa) is right
https://goo.gl/maps/x6uKsBhrrCx
but Shinjuku is not Shinkansen stn so need transfering Omiya or last stop Tokyo.
https://goo.gl/maps/g6xNeynwJg22
https://goo.gl/maps/k91yvcgBFZG2
(btw Omiya and Tokyo Shinkansen very slow down no big different as time total)

Or fr Matsumoto take "LtdExp Azusa/Super Azusa" no need tranfering until Shinjuku operate numbers a lot like Shinkansen.
https://goo.gl/maps/womsQwUULmP2
(LtdExp Azusa/Super Azusa is not Shinkanen/high speed train)
https://youtu.be/huftUunwFnc

Or Exp(High)Way bus(need booking) also convenient back to Shinjuku directly fr Nagano stn.
https://www.alpico.co.jp/access/express/nagano_shinjuku/
(DEC fare updated yet but no big different no worry)
https://pbs.twimg.com/media/CfJXd0yVAAA3by6.jpg:large
Also fr Karuizawa(need booking) by different companies "Seibu/西武" or "Chikuma/千曲" bus.
http://www.seibubus.co.jp/kousoku/line/line_chikuma.html