Met Éireann has issued a status yellow snow and ice warning which will take effect from 4pm today.
Forecasters said there could be a flurry of the white stuff on Friday and overnight into Saturday.
SNOW could be on the way according to forecasters at the Met Office.
They are forecasting north, northwest counties and areas on higher ground to be the worst affected but the entire country is at risk of snow.
"It will be cold for the next 10 days, with temperatures hardly making it up to 10C during the day", said Mr Eagleton. Temperatures will be low and it will stay cold for most of next week.
Motorists are urged to drive with care in today and tomorrow as a snow and ice warning is put in place for Donegal. A status yellow wind warning will also be hitting Donegal, as well as other Western counties including Galway, Leitrim, Mayo, Sligo, Clare and Kerry.
Northwest winds of 55 to 65 are expected to gust 100 to 110 km/h - strongest winds in coastal areas and over high ground. Highest temperatures of 3 to 6 degrees are forecasted.