Met Éireann has issued a warning saying that temperatures could plummet to as low as -8 overnight.
Road users are being urged to exercise extreme caution tonight and tomorrow morning.
Met Éireann has warned that paths will be slippery and roads will be treacherous due to the accumulation of ice and snow.
Temperatures are expected to drop to -4 on Monday and snow will be slow to clear in certain areas.
Gritters have been out in force since the cold snap began on Friday.
The long range weather forecast from Met Éireann indicates that Tuesday will be dry and sunny with rain in the afternoon.
Temperatures on Tuesday should be warmer than they have been for some time. Wednesday, Thursday and Friday are expected to be cool and windy.