More than 120 schools were forced to close across both counties, including 103 in Cornwall, amid heating failures and school bus cancellations.
Drivers faced treacherous driving conditions after temperatures plunged on Dartmoor in Devon.
Some main roads were closed amid a series of minor accidents, mainly in the worst-hit north and north-east of the area.
Police declared the situation in north Devon as a "critical incident".
Many bus services were suspended, burst water mains were reported, waste collections were postponed and the Eden Project in Cornwall was closed because of the weather.
The Met Office predicts the cold snap will last for at least the remainder of this week.
Carol Williams, the director of service improvement and professional practice with NHS Cornwall and Isles of Scilly, said: "People need to think about the necessity of their journey and the routes they are taking.
Forecasters expect the cold snap to last all week
"Well trodden paths may well be safe but falling on to a hard road covered in ice is painful at the very least and could possibly result in broken bones.
"The elderly are particularly vulnerable and I would urge people to delay their journey until the ice has melted or ask friends, relatives or neighbours to help get shopping essentials or run errands.
"The ambulance service and the NHS are always busier in the winter and the extra strain on services caused by slips, trips and falls makes this time of year especially difficult."
Devon County Council said its fleet of gritters were on full alert and would respond to any snowfall overnight.
It said gritters were prepared to work constantly to keep primary roads as clear as possible, but added that minor roads and estate roads will remain untreated and could be treacherous.
Cornwall Council's emergency planner, Richard Fedorowitz, said that the council was monitoring conditions and working proactively on A and B routes to make them usable.
But he added that conditions could be so changeable that if anyone did decide to travel they should do so with "extreme caution".
Some schools said they were to remain closed on Wednesday because of both weather and school heating problems.
In Cornwall, they include: Launceston College, Pencalenick School in Truro, Portreath Primary School, St Michael's Infants School in Helston, St Neot Primary School, and Trekenner School at Lezant.
About 20 schools in Devon are also staying closed, including: Bampton School, Bideford College, Diptford School, Duchy College, Lamerton Primary, Tavistock College, Tavistock Community Primary and West Buckland School near Barnstaple.
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