Snow showers could return on Wednesday and there is a risk of further disruptive snow and ice to parts of the country towards the end of the week.
Further warnings have been issued for most of England and Wales on Thursday and Friday, taking effect from 1pm on Thursday until 9pm on Friday.
The current warning in Scotland, Northern Ireland and most of the United Kingdom runs until 11am on Wednesday, while the South East, London and East Anglia are covered until 12pm.
A spokesman for the Met Office said: "After a frosty start, Tuesday will be cold and start dry".
The Met Office has issued a yellow warning of snow and ice for much of Scotland which is in force until noon on Tuesday. Some snow showers are possible from 4pm until the evening here.
Large parts of the country woke up to frost on Tuesday morning.
Temperatures are expected to drop as snow falls across the UK.
The disruption caused by the snow is set to deepen with a weather system arriving from the South West and pushing north on Thursday.
Paul Gundersen, the Met Office's chief meteorologist, said: "As the moist air from a weather system bringing storms to France clashes with the cold air sitting over the United Kingdom, it brings the chance of wintry showers and snow disruption to most parts". 10cm is possible in places, though there is uncertainty at this stage on where is most likely to see the greater snowfall accumulations.
Sleet showers are also predicted for between 5pm and 7pm and after 11pm, while snow showers have been forecast for between 12am and 3am on Friday morning.