from above :
Come Let Us Anew
"When All Men Sing" 
"I Wish New Year's Was Twice a Month"
Si Kahn - New Year
The January Man. Winter Wonderland
Let it snow
Baby, it's cold outside
Here comes Suzy Snowflake
Ring It In, Ring In the New Year
The Goldfish Am A Funny Bird(--tune of Auld Lang Syne.)
"Song for A New Year".  - Ian Robb
"Da Day Dawn"
Deck the Halls
Miner's Dream of Home
(Please to see)The King, 
"A Guid New Year to Ane and A"
May Your Cup Always be Full by Ali Burns
Twelve Days of Christmas,
"Until the Dark Time Ends",
WILD MOUNTAIN THYME
A song for any day
The New Year Carol \'The old year now away has fled'.
The Day We Went To Rothesay-o \ "One Hogmanay at the Glesga Fair..."
wassails(various)
The Merry Minuet
Bob Zentz...end of another year.
NEW YEAR - Jehanne Mehta 
 Peace round (Rose, rose, rose, rose.) - Jean Ritchie


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 "Ukrainian Carol of the Bells," \ "Ring Silver Bells," \ Schedriwka
A New Year Carol
Deck the hall
http://www.schooloftheseasons.com/carols.html