The wintry weather is set to begin today and run over tomorrow (Wednesday) and Thursday too.
A previous weather warning for high winds on Wednesday night is still in place, although it has been updated to say some southern parts could miss the worst of the conditions.
The wind warning covers England, Wales, Northern Ireland, and part of Scotland.
The Met Office has issued a yellow warning of potential travel delays, public transport disruption and power cuts, with some mobile phone services also likely to be affected.
People are also urged to be wary of icy roads and pavements, increasing the chances of accidents or injuries.
The largest accumulations of snow will be over high ground, with more than 10cm building up above 200 metres.
Thundersnow is forecast across western Scotland in particular and up to eight inches of snow could fall on high ground above 100-200m in Scotland.
There is also a weather warning for snow and ice starting early on Tuesday and lasting until 11am on Wednesday. Around this proper low, will be heavy rain and the likelihood of heavy snowfall on the leading edge which will head over the Pennines into Scotland.
Snow showers are expected during Wednesday evening before a spell of more persistent and possibly heavy snow develops in places during Wednesday night, with strong winds expected.
A warning for strong winds, gales and potentially stormy weather midweek with more snow.
The showers will be most frequent in Atlantic coastal counties, Met Eireann added.
"When you factor in wind chill, it will feel close to freezing", Burkill said.
'The snow will initially hit many northern and western areas and persist over several days, before impacting many other parts of the country at times during next week.