The Met office says the public should be aware of the risk of disruption to travel after sleet or snow showers continued to affect parts of the region on Sunday night.
Longer spells of snowfall were expected overnight and during Monday, with ice also affecting some roads.
"A very cold easterly airstream will continue to bring wintry showers across much of Northern Ireland," a Met Office forecaster said.
"In coastal areas the showers will be a wintry mix though heavier showers will fall as snow with a 1 or 2cm possible. Further inland 2 to 5cm of snow may accumulate and on higher ground above 200m perhaps up to 10cm."
Snowfalls of 3 to 6cm are also possible in the Republic of Ireland.
The Roads Service has urged motorists to exercise caution, particularly when driving on untreated roads.
"Salting of those roads on the scheduled salting network considered at risk from frost, ice or snow is planned," a Roads Service spokesperson said.
"Our engineers will continue to monitor conditions and further salting will be carried out where required."
Belfast International airport remained open and operational on Sunday. A spokesperson said adverse weather in other parts of the UK could affect some flights.
"Passengers who are due to travel should contact their airline for the latest information on their flights," the airport said.
The runway at George Best Belfast City airport was closed temporarily for snow clearing on Sunday but has since reopened.
Many domestic flights have been cancelled and passengers are advised to check the status of their flight before travelling.
Thousands of passengers have been left stranded at London Heathrow airport where flights were cancelled for a third consecutive day.
A total of 260 flights were cancelled on Sunday, 20% of Heathrow's usual business, and 10% of flights will not operate because of expected low visibility on Monday.
A spokesman said: "It is possible that weather conditions at other European airports will increase the number of cancellations.
"Passengers due to travel tomorrow are urged to check the status of their flight with their airline before travelling to the airport."
Around 3,000 homes were affected by power outages as heavy snow hit Northern Ireland on Friday.
It will become drier and brighter on Wednesday and Thursday, with lighter winds and some sunny spells developing.