More than 280 schools in Northern Ireland are closed on Wednesday because of heavy snow.
The Met Office said it expected a gradual improvement through the day. It issued a yellow warning for snow from 18:00 GMT on Wednesday till 06:00 on Thursday.
A further yellow warning for snow and ice is in place from 09:00 GMT on Thursday to 24:00 on Friday.
Northern Ireland Electricity said about 600 customers remained without power.
Delays on roads are possible, however, and drivers are urged to take care.
The Department for Infrastructure salted the roads overnight with snow ploughs operating where necessary.
"Resources are currently focussed on road salting operations, however, we will endeavour to restock salt bins and salt piles on public roads for community self-help as quickly as possible and when safe to do so," it said.
The department said a multi-agency group was meeting on Wednesday to monitor the weather and make emergency planning arrangements.
"Despite our best efforts we cannot guarantee ice-free roads even after salting and rain can wash salt off the road and ice may form," it cautioned.
By Geoff Maskell, BBC News NI weather presenter
Where the snow was lightest overnight - with just a couple of centimetres of lying snow - we have seen a slight thaw through the early hours of this morning.
However, the wet and slushy roads do not necessarily make the driving conditions any easier and a YELLOW severe weather warning for snow and ice remains in place after the earlier AMBER warning expired at 08:00 GMT.
Through the day, wintry showers will top up the levels where there is lying snow and some areas have a considerable covering.
At 05:00, the weather stations at Glenanne, Lough Fea and Ballypatrick were recording snow depths of 22 cm, 14 cm and 11 cm respectively.
The wintry showers will turn increasingly to rain by the afternoon.
However, the winds are building and there is the potential for gusts of 60-70 mph quite widely on Wednesday evening, perhaps reaching 80 mph in some places.
Along with the strong winds, a spell of heavy rain can also be expected, turning to snow for a time with the potential to add another 2-8 cm to snow depths in some places.
Translink suspended all bus services on Tuesday night, but services resumed on Wednesday morning.
Its rail services were continuing to operate, although delays are expected throughout Wednesday.
There were also delays to air travel because of bad weather, although Northern Ireland's three main airports were operating as normal on Wednesday morning.
The Rathlin Island ferry has cancelled all of its Spirit of Rathlin sailings on Wednesday. Rathlin Express sailings have been cancelled until 14:00 GMT when a decision will be made regarding a crossing later in the day.
Overnight, the Maritime and Coastguard Agency assisted the Southern Health Trust in using 4x4s to transport nurses to vulnerable people who were snow-bound in the Warrenpoint and Newry area.
Wintry conditions on many roads throughout the country this morning. Please take care if driving and leave yourself plenty of time for your journey. Please also keep distance between you and the vehicle in front even on roads that appear to be clear.— PSNI North Belfast (@PSNIBelfastN) January 17, 2018
About 23,000 customers had been without electricity at some stage on Tuesday.
Cavan and Monaghan
Storm Fionn brought heavy snow to the Republic of Ireland, where an orange snow and ice warning is in place until 12:00 local time on Thursday.
About 2,000 homes, farms and businesses in counties Cavan and Monaghan are without power.
The Republic's Road Safety Authority has urged motorists to take care on the roads, particularly drivers of high-sided vehicles during the strong winds.
Wednesday night's Gaelic football Dr McKenna Cup semi-final between Donegal and Armagh has been postponed following a pitch inspection in Ballybofey, County Donegal.
The game is now expected to be played at the weekend.
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