Icy paths and roads have made walking and driving difficult
UK transport is "as good as could be expected" given the freezing weather, Lord Adonis has said - as talks go on over how to preserve road salt stocks.
The transport secretary has indicated councils may have to cut salt use by more than the 25% already agreed.
Roads remain treacherous because of ice in many areas, with Northants and Flintshire councils among those reporting critically low grit reserves.
Up to 20cm (8in) more snow is expected in south-west England and south Wales.
Met Office weather warnings are in place for those areas, while parts of central and southern England could also see more snow overnight.
However, BBC weather forecaster Susan Powell said, for most of the UK, Tuesday would stay cold and grey, with a chilly wind but less snow than in recent days.
Temperatures in England and Wales would be just above freezing and about 3C or 4C (37F or 39F) in Scotland and Northern Ireland, she said.
A-level, AS-level and GCSE exams are continuing across England, Wales and Northern Ireland, with the number of school closures - about 850 UK-wide on Monday - much lower than feared.
Exams watchdog Ofqual said indications were that most centres had been open for tests or had made alternative arrangements for candidates. No exam boards have so far reported any test centre closures.
On the roads, the Institution of Civil Engineers has said the continuous cycle of freezing and thawing could contribute to the additional problem of potholes - particularly on roads where long-term maintenance had been neglected.
However, road salt remains the more pressing issue with the institution warning that supplies are "running dangerously low". The Highways Agency's insists they are sufficient to keep main roads open in the coming days.
Councils agreed last Friday to reduce the amount of salt being spread by 25%.
The Conservatives accused the government of inadequate preparation, equating the rationing to an "admission of guilt", while the Lib Dems want a review of the recommendation that local authorities hold a six-day supply of salt.
The Salt Cell, which brings together agencies responsible for supplying salt and gritting roads, is meeting to decide whether further cuts are required.
Lord Adonis updated the Cabinet about the situation on Tuesday morning, said BBC political correspondent Carole Walker.
The transport secretary was considering extending the relaxation of drivers' working hours to help the supply of salt - a measure already undertaken to help milk deliveries, she added.
Travellers are likely to face more disruption on Tuesday, albeit less severe than in recent days.
- First Capital Connect is running a 70% service, with 17 trains undergoing repairs for ice damage. The Thameslink Bedford-to-Brighton route has also been hit
- Five other operators' services - including Eurostar - were disrupted, including East Coast trains between Inverness and Perth, Edinburgh and Glasgow, and Leeds and London Kings Cross. Local services in Manchester, and those linking the city with Scotland, were also affected
- British Airways said flights in and out of Heathrow and Gatwick airports continued to be disrupted by the weather. Easyjet said there were no weather cancellations on Tuesday
- Fifty-minute delays affected the A38 north of Derby, where the northbound carriageway was closed after a crash, while two lanes of the westbound M20 near Maidstone in Kent were shut
- The A66 in both directions between A685 (Brough) and the A67 (Bowes) is closed because of snow, as is the A628 (Woodhead Pass) in both directions between A57 and A616
EU rules on how long milk tanker drivers can work without a break were temporarily relaxed to help delivery firms cope with weather-related problems.
Some dairy farmers have had to pour milk away after running out of storage space because tankers could not access them in the cold weather.
David Cotton, vice-chairman of the Royal Association of British Dairy Farmers, said the move would help.
"If you get held up somewhere because of an accident, you're just sat there and then you run out of driver hours, then you can't go and collect the milk."