A new warning of heavy snow has been issued across Wales for Monday, with up to 10cm (4in) possible in places.
Forecasters say a band of snow is expected to move eastwards, with 2-5 cm (0.8 - 2in) likely, and about 20cm (8in) on high ground.
However, the Met Office said there was "considerable uncertainty" about the "extent and depth" of the snow and urged people to watch for updates.
It follows earlier warnings of severe icy conditions on Sunday across Wales.
Motorists in Wales were urged to take extra care after plummeting temperatures left many roads treacherous as the freeze continues following snow on Friday and Saturday.
Health officials in several areas have called on off-duty staff to work to relieve colleagues, and asked for volunteers with 4x4 vehicles to ferry staff.
The Met Office said: "There is a continuing risk of widespread ice on untreated surfaces during Sunday afternoon, Sunday night and Monday morning."
"The public are advised to take extra care and refer to Traffic Wales for further advice on road conditions."
However, the Traffic Wales website was not working for a time on Sunday morning, although it was later up and running. Anyone seeking information can also call 0845 6026020.
Cardiff and Vale University Health Board said it had "tremendous support from a variety of agencies and volunteers" with 4x4 transport to take staff in and out and support people being discharged from hospital.
The board said demand for 4x4s was likely to be as strong on Sunday, and thanked the continued support of those involved.
Another health board, Cwm Taf, which covers the south Wales valleys, said it had had an "overwhelming response" from volunteer drivers.
"The response and community spirit was overwhelming and the volunteers played a significant part in getting our staff to and from the main hospitals," said Cwm Taf.
"We are extremely grateful for your help. We would also like to thank our staff who are working tirelessly to make sure that services continue to run as usual."
Many Welsh sporting fixtures on Saturday were hit by the weather, including Cardiff City's home Championship match against Burnley.
Rugby game on
However, while that game at the Cardiff City Stadium was cancelled, rugby side Cardiff Blues' Heineken Cup game with Northampton at the same venue will go ahead on Sunday (1500 GMT kick-off).
Cardiff Blues said: "Cardiff City Stadium staff have worked tirelessly to the early hours of Sunday morning to ensure that the snow was cleared off the pitch and the car parks."
Bus company First Cymru said its Swansea to Cardiff Greyhound service resumed as normal, with departures every two hours until 1800 GMT. National Express services from Swansea also resumed.
Dyfed-Powys Police said all roads in their area were passable with care, while North Wales Police said while surfaces were icy, conditions had improved.
The Gwent force said the Caerphilly mountain road was only passable with a 4x4, and, like South Wales Police, said driving conditions remained quite poor.
Breakdown services said Wales had been one of their busiest areas on Saturday, with abandoned cars adding to disruption.
Cardiff Airport said that while all its flights were on schedule, weather problems at other airports could mean cancellations or delays.
Travellers were asked to visit the arrival and departure live flight pages on the Cardiff Airport website for details.
The assembly government's 24-hour "snow desk" is running. It says it has enough road salt, with more stock due in a week.
The University Hospital of Wales in Cardiff, University Hospital Llandough, Royal Glamorgan at Llantrisant, Prince Charles in Merthyr and Ysbyty Gwynedd Bangor all asked off-duty staff to go into work if possible to relieve colleagues.