Local MP Alun Cairns said he was "very concerned" at the prospect of some school closures.
"They will see more school closures, they will see a reduction in local services, " he said.
There had been fears in the past that school closures would affect absentee records.
BBC: Wales snow: Neighbouring Caerphilly schools open and shut
Mr. McNiff said he hopes this will stem the seemingly endless announcements of Catholic school closures.
There has been a wave of school closures in recent years in Hungary, as population figures fall.
Snow has been affecting many areas across Northern Ireland, leading to school closures and treacherous road conditions.
Any school closures will be listed on BBC Northern Ireland's digital text on the red button service.
Travel disruption and school closures are continuing for a fifth day amid more heavy snowfall across the country.
Parents in Herefordshire will now be alerted to school closures and transport disruption via a new automated system.
Widespread school closures have continued, with about 950 shut in Wales, 700 in Scotland and thousands across England.
Parents wishing to check school closures can look on Somerset and Bath and North East Somerset websites.
Parents have received an apology from Worcestershire County Council after the authority's school closures website crashed for an hour.
Jersey's Education Department said islanders should expect an announcement on school closures on BBC Radio Jersey after 06:00 GMT.
That saving will enable us to avoid damaging cuts to services such as school closures or increases in class sizes.
Some reductions are already biting in school closures to pay for free university tuition and in lack of infrastructure investment.
Hundreds of protesters also held a rally in the centre of Aberdeen, where about 10, 000 pupils were affected by school closures.
The Education Department said an announcement on any Guernsey school closures should be announced at about 07:15 GMT on BBC Guernsey.
Councillors in Shetland have voted to start consulting on nine school closures.
In Derbyshire and East Staffordshire there are more than 90 school closures.
Rows over, for instance, school closures will run on in many communities.
Officials emphasized that school closures are ultimately local decisions, which Superintendent Al Hambrick at the Sherman Independent School District in North Texas also stresses.
CNN: In time of swine flu, add sanitizer, tissues to school supply lists
Commuters woke up to the heaviest snowfall in almost two decades a month ago, followed by suspended bus services, icy roads and school closures.
There are school closures in most other areas of the country.
Bristol City Council said it had more than doubled the capacity on its website after the page containing information about school closures crashed on Friday.
By the 29th the severe conditions were beginning to cause widespread disruption, with hundreds of school closures and delays to road, rail and air journeys.
Travel chaos and school closures have hit south-west England and Wales.
The latest information on school closures can be found here.
Meanwhile, the number of school closures varies from borough to borough.
Winter Storm Nemo, which has already caused hundreds of flight cancellations and numerous school closures, did little to dampen the mood on Wall Street though.
School closures have been reported across south-west England, with 200 closed in Gloucestershire, 240 in Hereford and Worcestershire and all Bath and north east Somerset schools shut.
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