It is expected to be wet and windy later, with the possibility of flooding in places from heavy rain and melting snow.
The strongest winds are expected to be along the east coast, especially County Down.
Meanwhile, a Status Red alert has been issued in the Republic of Ireland.
This is for coastal and mountain areas of Donegal, Sligo, Mayo, Galway, Clare, Limerick, Kerry, Leitrim and Cork.
The meteorological service, Met Ã‰ireann says that wind gusts of 130-150km/hr are possible in exposed areas until midday on Thursday.
The Republic of Ireland's department of education has advised schools in affected areas to consider remaining shut on Thursday.
The National Emergency Committee in the Republic has advised people living on the west coast to avoid any unnecessary travel, watch out for fallen cables and to check on neighbours.
More than 2,200 homes in the country were without power just after midnight.
Dublin Airport has reported some delays to flights.
NIE has warned of a possibility of damage to the electricity network, especially in exposed and coastal locations.
It says it has initiated an escalation plan and has emergency crews, engineers and call handlers on stand-by.
It has reminded customers that if they do lose electricity supplies they should contact the NIE Customer Helpline on 03457 643 643 or report the fault online.
Julia Carson, NIE Communications Manager, said: "If there is any damage to our network from severe weather, our emergency crews will be in position to get customers back on supply as quickly as possible, consistent with safety, and we will keep customers regularly updated and informed.
"We are particularly keen to stress our safety message to stay well away from broken power lines or electricity poles and report any damage immediately.  If you are without power, make sure you take a few simple precautions to keep you and your family safe."
Trafficwatch Northern Ireland reported on Wednesday that the Hall Road/Donaghcloney Road, in Lurgan, County Armagh, was closed due to a tree that was in a dangerous position.
Belfast City Council tweeted that it had closed Victoria Park because of the weather and that it will be closed for part of Thursday morning.
The adverse weather has led to a number of ferry cancellations.
BBC Northern Ireland weather presenter Cecilia Daly said that it would be wet and windy later with "snow initially in places slowly but surely turning to rain".
With a slight thaw, there is the possibility of flooding in places from heavy rain and melting snow.
The strongest winds are along the east coast especially in County Down with the possibility of trees coming down.
Overnight, rain is expected to clear and the strongest winds are forecast for the north and north-west with gusts of up to 70mph and possibly 80mph forecast by Thursday morning.  It is expected to be colder again, with wintry showers.
It is forecast to be very windy and stormy on Thursday especially in the morning with the possibility of damage to trees, power lines and travel disruption.
The wind warning in Northern Ireland is valid until 23:50 GMT on Thursday, with the Met Office providing updates.
Northern Ireland Electricity (NIE) has warned of possible damage to the electricity network, as wind gusts of more than 70mph are forecast.