For example, in this video from 2:00 onwards, the Prime Minister of New Zealand says "woman/women" several times. The context shows clearly that she means the word to be plural, but she says "woman" every time - or to look at it another way, she pronounces the plural the same way that "woman" would usually be pronounced.

My question is, is it usual for the two words to sound indistinguishable in NZ English, or is this perhaps just a particular local dialect?

Also, do New Zealanders sometimes write "woman" when they're referring to the plural (in the same way that "sheep" and "deer" are the written plurals), or is this just a pronunciation characteristic that doesn't show up in writing?