From Monday's midday chart on Ogimet - there's a massive low to the east of Fiordland. On current models this deepens over the next couple of days, pressure in it's centre gets down around 960 hPa. It moves across to the east and a little further south - the red arrow I've scribbled on the chart gives a rough idea where it's going and gets to by Wednesday.
As this thing goes across, gale force westerlies along the west coast are indicated, more rain and snow likely too. Its going to leave us with a strong south to southwesterly flow beginning on Tuesday, so could get very cold.
As ever with big low pressure systems, things can change rapidly, so we'll have a look at what the models show this thing is doing in the next day or so to get a better idea of this is still looking as potentially nasty as it is, better, or nastier.