Met Eireann has issued a yellow weather warning for snow and ice for tonight and much of tomorrow morning.
Showers of snow are expected at times, particularly on hills, mountains and areas of high ground in the western half of the country.
Temperatures are likely to fall below freezing nationwide tonight and hazardous driving conditions should be expected.
Showers are expected to turn to sleet and snow, with showers being heaviest and most frequent in the western half of the country.
The rest of the week is thought to be cold also with it turning milder by next weekend.
Tuesday to Thursday is expected to be cold with northern winds making it feel even colder.
When travelling in ice and snow, drivers are reminded to watch out for "black ice", use dipped headlights, decrease speed smoothly and leave extra distance between them and the vehicle in front.
Showers of snow are forecast this evening and tomorrow morning. Conditions will be worst in the western half of the country. Drive with care pic.twitter.com/sjZUI31SMe— RSA Ireland (@RSAIreland) March 20, 2017
Pedestrians and cyclists are advised to wear a high visibility jacket or reflective armband.