Met Éireann has issued orange and yellow weather warnings for snow and ice across parts of the country.
Wintry showers overnight have made driving conditions difficult and the weather forecaster said there would be showers of rain, hail, sleet and snow on Tuesday, with accumulations of greater than 3cm even on lower ground. Widespread frosty and icy conditions will develop, the forecaster said.
A snow and ice warning is in place for Munster, Dublin, Carlow, Kilkenny, Louth, Wexford and Wicklow.
The worst affected areas are in Connacht and the midlands. Met Éireann said. It warned that care was needed on all routes on Tuesday morning and said particular care was required on secondary and minor roads.
In Meath, gardaí urged HGVs to avoid Slane village following heavy snow. Snow was also causing problems around Kells. Heavy snow also left slippery conditions around Mullingar and black ice was reported around Tullamore.
In Tipperary, there were dangerous driving conditions around Thurles, Cashel and Nenagh, AA Roadwatch said.
Extremely dangerous driving conditions were also reported around Castlebar, Co Mayo.