"The pohutukawa tree (Metrosideros excelsa) with its crimson flower has become an established part of the New Zealand Christmas tradition. This iconic Kiwi Christmas tree, which often features on greeting cards and in poems and songs, has become an important symbol for New Zealanders at home and abroad." (NZ History.net)
One of the most popular Christmas carols in New Zealand is "A Pukeko in a Ponga Tree", which is a reworking of "The Twelve Days of Christmas".
You can listen to it here: http://folksong.org.nz/nzchristmas/pukeko.html
Here are some more websites about Christmas in New Zealand:
New Zealand.com: http://www.newzealand.com/travel/media/features/four-seasons/summer_new-zealand-christmas-experience_feature.cfm
NZ History Online: http://www.nzhistory.net.nz/culture/kiwi-christmas