A status yellow snow and ice warning has been come into effect for Cavan, Donegal, Monaghan, Leitrim and Sligo.
Met Éireann said there would be lying snow and freezing temperatures tonight.
Falls of sleet and snow tomorrow morning could produce some temporary accumulations, the forecaster added, leading to hazardous conditions on roads and paths.
The alert will continue until midday tomorrow.
Meanwhile, there is a status yellow rain warning for tomorrow and the early hours of Thursday for three counties in Munster.
Met Éireann said that prolonged rainfall in Cork, Kerry, Waterford could result in localised flooding and difficult travelling conditions.
The alert is valid from 4pm tomorrow until 6am on Thursday.
Earlier, the UK Met Office issued a yellow rain warning for Northern Ireland for tomorrow and Thursday.
It said a spell of persistent rain may cause difficult travel conditions and make journey times longer.
The warning takes effect at 2pm tomorrow and will last until 10am on Thursday.