A Met Office yellow alert for snow and ice for Scotland and Northern Ireland will kick in at 6pm, signalling three days of "frequent and heavy hail and snow showers".
Snow will be dumped up to 10cm deep in higher parts of Scotland and Northern Ireland, and between 2cm and 5cm elsewhere, according to the forecaster.
The Met Office also warned of possible travel delays and "a small chance that power cuts will occur and other services, such as mobile phone coverage, may be affected".
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England and Wales will not be spared the downturn and are expected to be lashed by strong gusts which could reach gale-force in some areas.
Met Office forecaster Matt Box said: "A cold front will come down on Monday and it will herald the arrival of polar maritime air mass across the UK and, that being a cold air mass, temperatures are going to feel a lot colder.
"It is also going to be accompanied by some cold winds as well, gale-force winds at time across the south, mainly coastal sites and exposed hills.
"There are going to be some blustery snow showers moving in from the west and bringing snow across Scotland at first."
By Tuesday the snow will have begun to reach the north of England and Wales, potentially moving further south for a time and leaving between 1cm and 2cm, Mr Box added.
Temperatures are not expected to escape single figures until the cold snap clears towards the end of the week, dipping towards freezing in Scotland on Tuesday.