Police are urging people to stay in their cars to keep warm after around 20 cars were abandoned on Cornwall's A39 dual carriageway amid heavy snow.
The extreme temperatures has seen the River Dee in Aberdeenshire freeze over.
Snow levels are likely to reach 1-3cm but there is a possibility for as much as 5-10cm. Blizzard conditions caused serious travel disruption this evening which saw up to 12cm of snow fall in Cornwall in just a few hours.
Snow in South Wootton on January 30, 2019. There will be strong winds with ice and frost forming as temperatures hit zero.
Magilligan, County Londonderry, falling to -8.5C (16.7F).
It will run its "winter weather timetable" on Friday - with passengers warned of peak services being busier than normal because of changes to some train times.
The ice and fog warning is valid until 11am on Thursday.
Media captionFive handy winter driving tips What warnings are in place?
The Met Office adds: "Snow amounts will vary markedly across England and Wales with many places seeing very little accumulating snow".
'The highest snowfall accumulations are likely to be in areas above 150 metres or so'.
"While I understand that Met Éireann and the Met Office operate two different standards in relation to weather warnings, I don't believe these competing approaches should lead to an inability to represent weather situations when/where they occur across Ireland".
Councillor Sharon Duddy described her concern as the cause of "great frustration" and called upon Met Éireann to revise protocols when communicating future weather warnings and forecasts. Road and air transport organisations help mitigate possible disruption by taking winter maintenance actions, such as gritting and ploughing.