The cold snap affecting the country brought rare snowfall to the seaside town of Paekakariki, north of Wellington, on Monday night.
Snow also fell in Featherston in the Wairarapa, and on State Highway 2 - the Rimutaka Hill Road.
MetService forecaster Paul Bruce said a thunderstorm in Cook Strait drifted northwards along the Kapiti Coast, which enabled the snow to get to low levels.
Police were urging caution on the Rimutaka Hill Road because a further five centimetres of snow could fall there on Tuesday.
There was snow to low levels in coastal Canterbury, north of Ashburton.
Sergeant Barry Hansen of Christchurch police says intermittent snowfalls made conditions treacherous overnight across Canterbury.
Part of the Lyttelton tunnel was closed because of a slip. Dyers Pass Road and the Summit Road in Christchurch were closed on Tuesday morning.
In the South Island, State Highway 87 from Outram to Middlemarch in Otago was closed, and chains were essential on State Highway 73 from Arthurs Pass to Otira.
Heavy rain warnings have been issued for the south and east of the South Island, and for southern and central parts of the North Island.
MetService says the Central North Island Plateau can expect snow down to about 500 metres as the storm moves north.
Nelson power cuts
Repair crews are working to reconnect about 60 households in the Nelson Lakes area after heavy snow brought down power poles over the weekend.
Contractors are attempting to restore 24 power poles between Glenhope and Kawitiri, about 80 kilometres southwest of Nelson.
United Group's area manager, Bill Allison, says contractors are using a helicopter to navigate the area, which is under half a metre of snow in places.
Mr Allison says much of the work has been completed, but some residents may not have power back until the weekend.