There certainly are Mistletoes in New Zealand (and Australia). I have no idea what that is in your picture, there really isn't enough detail.

I'm attaching a link to site that may help you a little (I hope).

Dee.

Here is a link that might be useful: Mistletoe in NZ

Hello Deejaus
Thanks for the link! It is mainly about the the mistletoes in the New Zealand Bay of Plenty, which is in the north of the North Island, some distance from the Abel Tasman Park (South Island), but also gives interesting facts about the New Zealand mistletoes elsewhere.
I have also received a splendid link about the New Zealand mistletoes in general, it might interest you:
http://brianmasontrust.org/mistletoe.htm
And, there being so many indigenous NZ mistletoes, my questions have become more or less academic: I suppose the picture really does show indigenous mistletoes, and exact identification of the parasite and the host plant will be difficult.
I am really impressed with the flowers of your mistletoes (here, the colourless flowers can hardly be seen with the naked eye, and pollination is carried out by the wind).
Many thanks.

You're welcome.
Thank you for the link you included. It is very interesting.
If you have better photos of your Mistletoe in question, perhaps you could send it to the email address on that site. They will be far better equipped to id it for you.
Good Luck!
Dee.

Hello Dee,
Good suggestion, but - there are two mail addresses on that site, my mails bounce from both of them (apparently, no longer in use).
And I found no other NZ sites to mail to on this subject.
I will try to post a better picture, but, as you can imagine, a picture taken from ground level won't show a detailed mistletoe.
Thanks anyway.
{{gwi:366782}}

Some useful other sites (not NZ specific) that might give you some extra information are:
http://www.anbg.gov.au/mistletoe/ (lots of interesting articles)
http://www.northqueenslandplants.com/Amyema/loranthaceae.html
You are very lucky that your native mistletoes have such wonderful flowers - much better than our boring UK one.
I have been trying (unsuccessfully) to get fresh seed of Au/NZ mistletoes to try growing them here on greenhouse shrubs. Unfortunately seed companies do not seem to think them worthwhile.