The Met Office yellow warning has been extended to 9am on Tuesday, with drifting and temporary blizzard conditions due in some areas.
Up to 10cm of snow is predicted to fall in places, as minimum temperature falls to -1C.
The Met Office says heavy, squally showers will spread through the night.
They are due to turn wintry on high ground and then increasingly to lower levels.
Showers are likely to turn to snow inland, particularly on ground above 100 or 200 metres in the gale force westerly wind.
The Met Office says accumulations of snow will be very variable.
"At lower levels, amounts of snowfall will be generally smaller and quite variable but some areas could see in excess of 5cm of snowfall, with some drifting.
"Winds will gust to around 50mph near the heavier showers but higher over hills," the Met Office warning continued.
The public should be aware of the potential for some disruption, especially to travel.
In Co Down, the A2 carriageway on the Belfast to Bangor Road has reopened after a fallen tree was cleared close to Cultra railway station.
Meanwhile, Garvaghy Church Road in Dromore, which was closed due to fallen power lines, has also reopened.
Amber "be prepared" warnings for snow have also been issued by the Met Office for many parts of Scotland, including the Highlands and Western Isles, Strathclyde, the south west, Lothian and Borders and Central, Tayside and Fife areas.
Meanwhile, an orange warning is also in place in the Republic of Ireland as severe gusts of wind are being experienced across the island.
"Westerly winds will reach strong to gale force, with gusts of 90 to 130km/h which may cause some damage," Met Éireann said.
"The strongest gusts will be in the west and the north of the country at first.
"The strong winds and snow showers will produce very poor conditions at higher levels, with the possibility of some blizzard like conditions."