"On Wednesday there'll be rain in western parts and it'll be getting to most places by Thursday," Adams told the Herald.
MetService reported that there is a possibility of rainfall reaching warning limits around Nelson, northern Marlborough, Taranaki, central North Island high country, the Gisborne ranges and eastern Bay of Plenty on Wednesday and early Thursday.
Conditions should settle again on Friday while arctic southwesterly winds swoop over the country, lowering temperatures. Overnight lows could get below 2°C, creating the right conditions for snow, Adams said.
He thought snow was a possibility down to 600m and could hit Canterbury, the far south, Southland Hills, southern Fiordland and southern Otago on late Thursday and Friday.
"It's all about catching the last of the rain. It has got to snow at exactly the right time.
"It is not currently looking like a lot of snow in a lot of places but lingering showers are likely to give a dusting of snow to the far south and Ruapehu."
The Arctic southerlies could be pretty strong and needed to be considered by high-country farms, which could see sub-zero temperatures, Adams said. Areas around Invercargill and Dunedin had the highest risk.
"People, especially farmers, can expect wintry conditions over the lower South Island, which may result in a wind-chill that can cause stress to livestock," MetService reported.