MET Eireann has warned that up to five centimetres of snow could accumulate in some areas tonight as temperatures are set to plunge.
A Status Yellow weather warning has been issued due to the cold conditions.
Today, daytime temperatures will barely rise above freezing, with peak temperatures of just 3C expected.
Snow falling overnight on Monday could lead to 5cm or more accumulating in some areas.
Air temperatures in areas where snow falls could plunge as low as -7C.
On Tuesday morning further snow is expected to fall in eastern parts of the country, however milder conditions will spread from the west over the course of the afternoon.
Wednesday also looks set to be a very cold day, with temperatures falling well below zero at night.
A Met Eireann spokesperson said: “It will be cold tonight with lowest temperatures of -1C to -5C leading to severe frost.
“Untreated road surfaces and paths will accumulate ice, becoming very slippy and quite dangerous.”
Motorists have been warned to expect poor road conditions this morning, with possible patches of freezing fog.
Meanwhile Forecasters in Britain are predicting the coldest night so far this winter.
Temperatures are expected to fall as low as -15C late tonight and early tomorrow morning in parts of inland Scotland.
Some areas have already experienced freezing conditions with the temperature dropping to -7.1C in Dalwhinnie in the Scottish Highlands last night.
Met Office operational forecaster Calum MacColl said conditions would be "clear as a bell" in affected areas and urged people to wrap up.
"It only has to get past -9C and we'll have the coldest night for winter," he said.
That record was set on December 27, in Cromdale, Moray.
Snow showers are also expected to push into coastal areas in the north east of Scotland but severe yellow weather warnings for snow and icy conditions covering large swathes of the country have been lifted.
Drivers have been warned to take extra care on the roads in icy conditions.
Additional reporting provided by PA