Japan uses the gregorian calender (I'm not sure when they adopted it), so the 
New Year's corresponds to the west.  There is also farmer's new year's, or 
little new years, which is celebrated around the fifteenth.

Now for some other corrections...

The wands with paper strips that the shinto priests use to purify worshipers 
is called "haraigushi" not "gohei.

The ablution pavillion that is visited to wash the hands and mouth before 
entering the shinto shrine is called the "temizuya".

"Toso" is a spiced herb sake that is traditionally served at this time 
(replace the sake with toso).

The 108 times the bell rings at the buddhist temple is to drive away the 108 
evil human passions.

The first three days of the New Years are national holidays.  To keep the 31st 
a holiday, I'll start school again on January 4th (by which time Ukyou should 
be back from visiting her parents).

Sorry for all these corrections, but I only got to do some research today.  
Working a construction job is good for paying bills, junk for getting off time 
to write these fanfics.

JK