The worst today's south-westerly flow would bring would be wet clothes on the washing line and bored, housebound kids.
Almost all of the North Island could expect showers, becoming more frequent as the front crossed the island during the afternoon and evening, Lee said.
The South Island would be similar, with showers and rain for the West Coast and southern areas.
That could turn to a few snow flurries down to about 500m in Southland and Clutha, with flurries also possible to about 800m in other parts of Otago.
A southerly change would bring a few showers through the Canterbury Plains in the afternoon and evening.
Only Nelson, Marlborough and Gisborne look likely to escape the wet, he said.
"There's a bit of an east-west split. In the west it's wetter weather in general, in the east it's drier weather in general."
Temperatures would be average for most, with a slight bump in the upper North Island.
Whāngārei, Auckland, Tauranga and Napier would reach 17C today, it will be 16C in Hamilton and New Plymouth, 14C in Wellington and Nelson, and 10C in Christchurch and Dunedin.
The south-west flow continued until mid-Tuesday, meaning similar conditions to today — although the southwesterlies would briefly become stronger going into Tuesday, delivering a wet start for much of the North Island and exposed eastern areas of the South Island.
Settled weather would arrive later on Tuesday, and Wednesday was likely to be cold, with overnight temperatures dipping below average for the upper North Island.
Auckland was likely to drop to 4C, half its average, and the Coromandel to 1C — about 6C below average. Lows in South Island centres would be around average, with 1C in Christchurch, 4C in Dunedin and 0C in Nelson, Lee said.
Thursday also look settled for most, but that wouldn't last — another low pressure system bringing wet weather is on it's way to the country late in the week.