Temperatures would be mild in the north - Auckland was expecting 21C, Hamilton 20C and Tauranga 23C, while Wellington would reach 16C.
At the same time, a cold front was coming up the South Island, bringing rain, showers and - in some places above 600 metres - snow.
Road snowfall warnings are in place for several South Island alpine passes, with rain expected to turn to snow early this morning on the Crown Range, Lindis, Arthur's and Porters' passes, and during this morning in Lewis Pass.
The front eases during the day before moving off to the east of the island, Coutts said.
It'll be a cold late-spring day - 14C is forecast in Christchurch and 13C in Dunedin.
Conditions would be similar tomorrow and Tuesday, with heavy rain possible in the east of the North Island and gale southerlies in the southern part of the island due to a strong southeast flow across central New Zealand.
The South Island would be fine in the west and south, with cloud and some showers possible in the east and north, he said.
The low would move away by the middle of the week, bringing relief for those tired of the sometimes sticky weather in the north.
"[There'll be] a southwest flow, so it'll be cooler and drier across the country."