Met Éireann issued the status yellow weather warning last night for scattered snow showers on Thursday, Thursday night and into Friday.
The Met Eireann website says that those wintry showers will be widespread and frequent in the north of the country with "accumulations of snow over lower ground". High-sided vehicles and motorcyclists are particularly vulnerable to strong winds.
Northwest winds will increase strong and gusty.
Snow is forecast to hit Peterborough at the weekend with temperatures set to drop sharply.
The warning will remain in place until 4pm tomorrow.
Accumulations of up to three centimetres are possible in parts while icy conditions are likely on the roads.
Met Éireann warn it will be "very cold again" on Friday, with a few sunny spells, but with occasional wintry showers of hail, sleet and snow. The north and northwest areas will be most at risk, but a slight dusting could occur in other parts, including Kildare.
Meanwhile, the Road Safety Authority has warned motorists to expect the unexpected with high winds and icy conditions.