The cold front moving across the South Island is set to sweep north over central New Zealand.
MetService says snow has already fallen to low levels in the South Island and further snow showers are forecast through Wednesday and Thursday in southern and eastern areas.
The falls could be as low as 100 metres at times.
Significant accumulations are likely at higher elevations and there could be an extended period of snowfall in the Kaikoura Ranges.
In the lower and central North Island, snow could come down as low as 400 metres.
MetService also says a low is forecast to develop east of central New Zealand during Wednesday and deepen rapidly on Thursday.
It would bring heavy rain and gales to the upper South Island and the lower North Island.
Interislander ferries are due to stop sailing from Wednesday evening, with 7m-high waves predicted for the Cook Strait through until Friday morning.
The NZ Transport Agency says the following stretches of highway have closed in Canterbury and Otago because of the snow:
* SH8, Fairlie to Lake Tekapo
* SH85, Becks to Wedderburn
* SH8, Omarama to Tarras (Lindis Pass)
* SH6, Hawea to Haast.