Parents have been advised that schools will make individual decisions on whether to open over the coming days,
The highest threat for Wednesday faces schools in Dublin, Carlow, Kildare, Laois, Louth, Wicklow and Meath where a status orange warning - the second most severe level - is in place for snow and ice until mid-morning on Wednesday.
Most schools will advise parents by text message, social media or through their websites about school opening.
In the event of severe weather or a status red warning over the coming days, there is a possibility authorities will advise large-scale closure of schools in certain counties, as occurred during Storm Ophelia.
A key consideration will be whether school transport and public transport will be able to bring pupils to schools safely.
In the meantime. Seán Hogan of the National Emergency Coordination Group said it will be for each school to consider whether it is appropriate to open.
“We have asked the schools to keep parents informed of their plans as early as possible,” he said.
Met Éireann forecaster Joanna Donnelly said a red warning was likely to be issued later this week.
"The warnings are in operation for Wednesday for the east coast for the accumulations that are going to come overnight tonight and for the early hours of the morning," she told RTÉ's Ray D'Arcy Show on Tuesday.
“They’ll be updated, the advisory is out there for the whole of the week and there’ll be more warnings issued.
“There will be a red warning issued, but we have to wait until we have all of the best evidence in front of us to look at that.”
However, Met Éireann told The Irish Times on Tuesday night currently "the evidence is not totally conclusive to issue a red warning".
Forecaster Joan Blackburn said “it is not definite a red warning will be issued”.
“Met Éireann is continually assessing the data from the different models and if there is enough evidence to issue a red weather warning we will do so,” she said.
Minister for Education Richard Bruton, meanwhile, said his department it will continue to monitor the situation as it progresses during the week and will follow any advice from the National Emergency Coordination Group.
A less serious status yellow snow and ice warning has also been issued for Kilkenny, Longford, Wexford, Offaly, Westmeath, Cork, Tipperary and Waterford, with snow accumulations of up to 3cm expected in some areas by Wednesday morning.
A “significant snow event” with possible blizzard conditions is forecast for Thursday evening, which is likely to cause disruption on a much greater scale.
Schools are unlikely to be required to cut short their holidays to make up for lost time as a result of closures linked to any closures according to senior sources.
Provisions set out in an official circular which offers guidance on unforeseen school closures state that school management bodies should assess whether schools can complete the curriculum before the end of the academic year.
It advises that shortfalls can be made up by prioritising tuition over other non-tuition activities, or ensuring State exam year classes attend all classes to the end of May.
Cutting short holidays would likely face stiff opposition and cause disruption to holiday plans for teachers, parents and students, say sources.
