More than 100 schools have been closed.
The Northern Ireland Ambulance Service (NIAS) said it was "experiencing difficulty in responding to some emergency calls" due to the weather.
"We would ask that people only call 999 in a real emergency and to remain patient if there is a delay in ambulance response," the NIAS said.
It said NIAS staff would "continue to prioritise calls on the basis of clinical need".
A number of Translink Metro bus services were also affected on Thursday due to the snow.
The Upper Hightown Road in Belfast has been closed because of poor road conditions.
Police patrols in the area appealed to the public to avoid the road and obey the cordon and diversion signs.
The Met Office said a yellow warning of snow and ice will remain in place until 11:00 GMT on Friday.
Parents of pupils at Loughash primary school, Dunamanagh, County Tyrone, are advised that the school will be closed on Friday.
Transport NI, formerly known as Roads Service, said that strong winds are also likely to combine with the snow to make conditions more difficult.
It said salting and ploughing operations are continuing.
Police have advised drivers to slow down, put their lights on, leave more room to stop than usual and brake gently to avoid skidding.
"Drive slowly on snow in the highest gear possible," a PSNI statement said.
"Do not assume your vehicle can handle all conditions. Even four-wheel drive vehicles can encounter trouble on winter roads," it added.
Places in the south east of Northern Ireland that do not have much snow will still be bitterly cold and will be at risk of ice, forecasters have said.
The cold weather will continue throughout Thursday and it will remain very cold until the beginning of next week.
Check out the latest travel news for Northern Ireland
For the latest on the roads visit the BBC's travel news page and keep up-to-date with the latest updates on BBC News NI's Live pages.
Alternatively, for regular travel bulletins listen live to BBC Radio Ulster and follow @BBCNITravel.
Below are a number of other traffic information sources.
Trafficwatch NII
Transport NI
Translink
@PSNITraffic

The hosts go into the final day on 199-6 in their second innings, a lead of 278 runs.
John Anderson top-scored with 59 while Ed Joyce (37), William Porterfield (29) and Gary Wilson (25) also contributed on a day when 45 overs were lost.
Tanveer Ahmed and Tanwir Afzal each picked up two wickets for the tourists.
The Irish play positively, scoring at a rate of around four an over in an attempt to force a result despite the best efforts of the Belfast weather.
Joyce scored a fluent 37 from 55 balls in an opening stand of 53 with skipper Porterfield and was unluckily dismissed when he hit his wicket.
Anderson and Porterfield added a further 48 before the captain was bowled.
Niall O'Brien (15) and Paul Stirling (six) both went cheaply, but Anderson's fourth half-century for Ireland ensured they were always on top.
The Merrion man top-scored before mistiming an attempted hook shot.
Gary Wilson scored a breezy 25 and was trapped lbw two balls before the umpires decided that the light was too poor to continue.
Porterfield indicated that Ireland would bat on Friday, probably hoping to set Hong Kong a target of around 330.
Play on the final day will start 30 minutes early at 10:30 BST, with a potential 104 overs.
Meanwhile, Ireland have brought North Down leg-spinner Jacob Mulder into their squad for two T20 games against Hong Kong at Bready next week.
He replaces Barry McCarthy, who is required by Warwickshire for their County Championship clash with Yorkshire at Headingley.
Snow showers are continuing to affect the road network across Northern Ireland on Thursday and there is also the risk of ice on roads.
[NEXT_CONCEPT]
Ireland remain in control against Hong Kong in the Intercontinental Cup game but they were frustrated by rain and bad light at Stormont on Thursday.