Status yellow weather warnings are in place, with Met Éireann issuing one snow-ice warning for Leinster, as well as Cavan, Monaghan, Leitrim, east Cork, Tipperary and Waterford.
The alert came into effect at 6pm and remains in place until 4am tomorrow.
Speaking on RTÉ’s Morning Ireland, Gerry Murphy of Met Éireann said that the snow overnight will "be enough to cause disruption".
He said that the snow will not be excessive but frost overnight could cause hazardous road conditions.
Low temperatures are set to be between -3C and -5C degrees in many places.
❄️ A snow-ice warning comes into force this evening for many areas ❄️ pic.twitter.com/XiF2Zq53g3— RTÉ News (@rtenews) February 5, 2018
Mr Murphy said: "This evening and for the early part of the night, until around 3am, between about 0 and 3cm, so not excessive amounts, but nonetheless enough to cause disruption.
"Once it clears later in the night, we will see freezing behind it. That frost will possibly make for very hazardous driving conditions overnight and tomorrow morning."
Wintry showers will develop in the west tomorrow morning.
The Road Safety Authority has advised all motorists to exercise caution when using the road.
It said that road users should check local weather and traffic conditions, and be aware of driving conditions before setting out on a trip.
Here is the rain/snow forecast for the next 24 hours from Met Éireann's high resolution model.— Met Éireann (@MetEireann) February 5, 2018
Rain = Blue to Red
Snow = White
Latest weather warnings herehttps://t.co/X6NncUghZ9 pic.twitter.com/hIT6QVFANX