Snow is falling in the deep south, covering Invercargill and some Dunedin suburbs, and more is forecast.

The alpine passes have also kept graders busy as a winter cyclone near Stewart Island sends temperatures plummeting, says WeatherWatch.co.nz.

More heavy snow is predicted for Tuesday night and Southland will still see flurries to sea level.

The West Coast is again being hit by temperatures well below the norm after a freak cold snap killed over 200 cattle near Hokitika earlier in June.

More snow is also predicted for the North Island's Central Plateau, including State Highway 1 on the Desert Road.

The snow is likely to ease later on Wednesday but ice may cause issues for the highway overnight Wednesday and for the next few days.

There will be strong winds for many areas on Wednesday with more squally showers and snow predicted, said head weather analyst Philip Duncan.

The winds are likely to strengthen significantly around coastal parts of southern New Zealand, mainly around the Catlins in Southland and coastal Otago, and push into Canterbury, especially Banks Peninsula.