Operations Manager Phil Marsh says it is likely some customers will be without power for another two to three days.
He says areas affected include Kaponga, Kapuni, Opunake, Okato, Oakura, Omata, the eastern suburbs of New Plymouth, Waitara and Inglewood.
And with the school holidays beginning today, Mr Marsh is urging parents to keep their children indoors.
"We are aware that we have multiple lines down due to this storm.
"Power lines should be treated as live at all times, and please ensure you keep children and pets away from these hazards.''
Power was also cut yesterday to 1700 customers after trees fell on powerlines in Lower Hutt and Wellington.
By last night, 103 were still without power in the suburbs of Miramar, Makara and Grenada.
Flights resume in and out of Wellington
High winds also affected flights in and out of the capital yesterday, with most cancelled or delayed.
Winds gusted to 106km/h at the airport.
A spokesman from Wellington airport said most scheduled flights were running this morning.
A few domestic services had been cancelled, but these were operated by smaller planes.
Some international flights had been delayed, but both Jetstar and Air New Zealand services were operating.
The airport would continue to monitor conditions through the morning, he said.
Ferry services resume: "It's going to be a rocky ride"
In the capital yesterday, winds reached 146km/h and a storm warning was in force for Cook Strait, with swells reaching up to 5m, according to the MetService website.
Interislander and Bluebridge ferry passenger sailings were cancelled because of the high swells in the strait.
Ferry services in the Cook Strait are expected to resume this morning.
A spokeswoman from the Interislander in Wellington said the 8.15am service had been delayed, but was expected to leave at 9.15am.
The 10.30am ferry from Picton was expected to leave on time.
Passengers who were supposed to leave on yesterday's cancelled ferries had been transferred to today's services, she said.
"The ships are full.''
Swells were expected to reach between 4.5m and 5m.
"It's going to be a rocky ride,'' the spokeswoman said.
The wild weather also caused a ship to break free from its moorings at Wellington's Aotea Quay. The Panama-registered car-carrier Trans Future 7 drifted into the harbour when the bad weather hit, CentrePort port operations general manager Steve Harris said.
The vessel had been loaded with vehicles before it broke away from its mooring, but they were in no danger of falling overboard.
Tugboats would hold the vessel in a "safe place" in the harbour until the weather cleared enough for it to sail to Lyttelton or back to its berth, Mr Harris said.
Extra care required on roads
Motorists across the country are being advised to take extra care this morning, with stormy weather causing havoc on roads in the North and South Islands.
Four roads remain closed due to hazardous conditions.
In the North Island, snow has shut the Desert Rd, with drivers being diverted through the National Park.
Further south, snow has also closed State Highway 94 between Te Anau and Milford.
State Highway 63 from St Arnaud to Renwick Road remains shut after high winds knocked trees onto the road overnight.
And a washout on State Highway 1 near Waipahi has also closed the road between Clinton and Gore.
The Transport Agency has urged motorists to drive to the conditions.
Many drivers would also need to carry chains due to icy roads, a spokesman said.
Even Auckland will feel the cold
Auckland will today endure one of its coldest days this year, with strong winds making a 6C high feel even icier.
The MetService says that with the wind chill factored in, it will feel more like 4C.
Today's temperature low will equal that of July 1, the second coldest day of the year after June 24, when the mercury fell to 3C.
Squally thunderstorms, hail and 100km/h winds are predicted for exposed areas of Auckland, the MetService said.
Don't worry - the bad weather won't last
MetService said conditions around the country would improve during the week.
"All of these showers, be they rain, snow or hail are going to slowly ease back through the day,'' meteorologist Dan Corbett said.
"The strongest winds have peaked but we're still looking for some strong gales across central parts of New Zealand.
"The whole low that's been bringing the southerly air stream is starting to move east through the day ... and the winds will slowly die down,'' he said.
And Aucklanders struggling with high winds and showers will be needing sunglasses by Friday, Mr Corbett said.
"Today we'll struggle to get to 10C, but by Friday we'll have sunshine and 16C.''
The big chill
Today
*Auckland: Fine spells and a few showers. Fresh cold southerlies. High 6C.
*Cold and wet weather to blanket much of the North Island.
*Snow down to low levels on the Central Plateau and the South Island.
Tomorrow
*Auckland: Fine with cloudy periods. High 13C and 6C overnight.
*Frosts in the central North Island. Showers for Wellington.
