The Met Office has issued a yellow alert that came into effect at 4pm on Sunday and will remain in place until 11am on Monday.
Temperatures could drop to as low as minus 5C in some areas on Sunday night, with hazardous icy conditions expected on ungritted roads and paths.
The forecaster warned that freezing fog and patches of ice are likely to lead to some slow or difficult journeys on Sunday night and into Monday morning.
⚠️ Yellow weather warning issued ⚠️
Ice and fog across Northern Ireland, SW Scotland and parts of England and Wales
The odd snow shower is also possible along eastern coasts, and maximum temperatures on Monday will be 3C.
The icy spell brings an increased risk of injuries from slips and falls on slippery paths, delays to bus and train services, and a chance of flight delays or cancellations.
The Department for Communities is to issue cold weather payments on Wednesday to people living in parts of Northern Ireland particularly impacted by the cold snap.
Payments of £25 are issued automatically to certain regions when the average temperature is recorded or is forecast to be 0C or below for seven days in a row.