Heavy snow has closed the Desert Road, in the central North Island on Monday night.
The New Zealand Transport Agency says detours are in place on State Highways 49, 4, 47 and 46. The closure is expected to stay in place overnight.
The MetService says 10 to 20 centimetres of snow is expected to fall above 700 metres on the Desert Road in the next 12 hours.
Four to eight centimetres of snow is expected to fall near the Rimutaka Hill Road summit by late on Tuesday morning.
The MetService said snow is forecast to reach warning levels in the hills of Wellington and in Wairarapa, Taihape and inland Whanganui.
Spokesperson Hordur Thordarson said conditions could make driving difficult.
"Snow could start to affect the higher roads in these areas later this afternoon and it's certainly likely to cause trouble for commuters. Even small amounts of snow will make the roads very slippery and difficult to negotiate."
In the South Island, the MetService expects a dusting of one or two centimetres for the Lewis and Porters passes, as well as for Milford Road.
Popular skiing peaks nationwide are expected to benefit, with snow and strong southerly winds forecast for southern Fiordland, Southland, Otago and Banks Peninsula.
The MetService said the Remarkables and Mount Ruapehu were looking good.