Most boys play the role of an arctic (white) hare while most girls are snowflakes.
True! Everyone was a hare or a snowflake (option: a squirell) at least once in his/her life. It's a given. ))))


Overall every young child did these things on New year "utrenik":
1) took part in "khorovod" (http://en.wikipedia.org/wiki/Khorovod) singing traditional New year songs "В лесу родилась елочка", or "Сколько на елочке..", etc.
2) helped Ded Moroz to save Snegurochka, o vice versa, or something along these lines
3) told a poem (sang a song) to Ded Moroz
4) got a present (usually a box/bag of candies and sometimes fruits).
5) had his/her picture taken under the New Year tree in a New Year costume (even if it's just a foil crown).

Usually parties in kindergardens are not grand events: just a small group of kids, their nurses and (often, but not always) parents. Ded Moros and Snegurochka are impersonated by the staff, parents or invited artists. Depending on the size of the organisation, which arranges a party for kids, and its wealth, it may be something small and simple or huge and professionally made.

VIDEOS:
Hey, rockzmom, you can watch a few "utrenik"s videos if you are curious. Dmitry whould "remember" something like that. I chose a few to start with (there are loads of them on Youtube, but they are very much alike).

1) First to get in the mood is a DANCE OF LITTLE SNOWMEN. The little guy to the left is hilarious. And I like the way grownups giggle at the background.
http://www.youtube.com/watch?v=tC11ym4GVKY

2) Here is a fairly typical 'utrenik" with almost all the elemets present. Can be interesting because of some pre- and post utrenik footage from 1:30, then an episode when children traditionally shout "1,2,3, lit up, fir-tree!"at 6:55. As it usually happens the lights don't go on the first time.. New Year suspense. At the end you can see the distribution of candies.
http://www.youtube.com/watch?v=VASoqImv3yg

3) Oh.. I've just found two more video from the same kindergarden. They are rather good. On the pros - LOTS of interaction with Ded Moroz, Snegurochka and fairy tales characters. On the cons - they are long (10 minutes), and the are not very conventional costume-wise (for some reason a lot of the girls are Red Riding Hoods. Weird). The kids in these are older, so the performance is a little better.

a) http://www.youtube.com/watch?v=3aQUalhAqFU
Ded Moroz appears around 3:20, and he sings well. Also at 5:00 there's a traditional khorovod + the most famous New Year song.

b) http://www.youtube.com/watch?v=ScyOc8au360
No need to watch all of it, I added it just because of a nice bit of the action: at 3:47 kids shout to prevent bad Wolf from stealing the presents, and then 'punish' him in a mock snowball fight.

That's all. I hope I didn't bore you to death. )))