A hospital consultant in Swansea has advised elderly people to stay indoors in the cold snap after dealing with a record number of fracture admissions.
Meanwhile, a primary head teacher called thieves "callous" after the school's heating oil was stolen.
Ysgol Rhewl, near Ruthin, Denbighshire, was one of 20 schools in Wales forced to shut in below-zero temperatures.
Water supplies to several thousand people in Rhondda were hit by freezing conditions affecting a treatment works.
There was also a spate of minor crashes on roads in south and west Wales.
SCHOOL CLOSURES FOR 7 JANUARY
Carmarthenshire: Ysgol Bro Banw; Ysgol Gynradd Cross Hands; Ysgol Feithrin; Ysgol Gymraeg Rhydaman
Ceredigion: Lampeter Comprehensive
Conwy: Ysgol Gynradd Betws y Coed
Denbighshire: St Brigid's School, Denbigh; Ysgol Borthyn, Ruthin; Ysgol Llanbedr Dyffryn Clwyd; Ysgol Rhewl, near Ruthin
Merthyr Tydfil: Ysgol Gynradd Rhyd y Grug
Powys: Newbridge Church in Wales School, near Llandrindod Wells
Swansea: some classes cancelled at Birchgrove Junior School
According to the Met Office, the severe conditions are set to continue for the next few days.
The weather has led to hospitals reporting a rise in patients with ice-related injuries.
Accident and emergency consultant Mike McCabe at Morriston Hospital in Swansea said his department had again been extremely busy, after dealing with 106 fall injuries on Monday.
Thirty patients had fractures and trauma injuries which needed them to be admitted - an unprecedented number in a single day, Mr McCabe said.
He said: "The clear message for elderly people is to stay indoors.
"Don't go outside to put the rubbish out, don't go out to put the cat out, don't go to the shop to buy a newspaper - instead get a fit and healthy relative or friend to run any errands for you.
"It's very icy outside, so stay indoors and keep safe."
Glan Clwyd Hospital saw 231 casualties in the 24-hour period to midnight on Monday.
Wrexham Maelor Hospital saw 212 patients during the 24 hours to 1500 GMT.
For both hospitals the usual average daily figure is around 150-170 patients.
Maelor hospital managers said many of the injuries were due to falls.
A surge in patients due to ice-related incidents was also seen in Ceredigion, Carmarthenshire and Pembrokeshire.
Hospitals which also witnessed an increase in patients were Prince Philip in Llanelli, West Wales General in Carmarthen, Withybush in Haverfordwest, Pembrokeshire, and Bronglais in Aberystwyth.
At the Royal Gwent Hospital in Newport, 39% of the 201 patients seen in accident and emergency on Monday were due to falls, but they were also very busy with treating chest pains and respiratory problems.
Aberdaron -2.4 °C
Aberporth -3.1 °C
Capel Curig -9.2 °C
Hawarden -6.3 °C
Lake Vyrnwy -7.0 °C
Milford Haven -3.8 °C
Mumbles Head -2.1 °C
Pembrey Sands -4.5 °C
Rhyl -5.6 °C
Sennybridge -8.1 °C
St Athan -5.0 °C
Trawsgoed -9.3 °C
Valley -3.4 °C
Sample temperatures, 0900 GMT on 6 January, Source: Met Office
Meanwhile, Dwr Cymru Welsh Water said freezing conditions had affected the water supply in the Rhondda, between Maerdy and Porth.
Water bowsers were being sent in and bottled water made available to mothers with young babies and those with special needs.
A spokesman said problems had "severely restricted supplies" feeding Maerdy water treatment works.
"As we carry out repair work, customers may experience intermittent loss of water supply and discoloured water. We are tankering water into the area to minimise the impact to customers."
The spokesman said they wanted to reassure the public that the water supply was still fit to drink.
Schools closed for a combination of heating problems and icy conditions.
Those affected were mainly in Denbighshire, Gwynedd and Carmarthenshire.
But the head of a 50-pupil primary school near Ruthin was angry after discovering its fuel supply had been stolen.
"The thieves have shown a blatant disregard for the pupils and staff's health and well-being," said Tania Armstrong-Owen, head of Ysgol Rhewl.
The fuel was taken from a tank outside the school over the Christmas holiday
"The oil is essential to heat up the school and what makes this crime even worse is the fact that we are experiencing the coldest snap of the winter so far. "
The fuel was taken from an oil tank outside the school sometime over the Christmas and New Year period but was only discovered on Monday.
As a result, the school, which has around 50 pupils, has been forced to close on Tuesday and Wednesday, with hopes of a fresh supply for Thursday.
In separate incidents, there were a series of road crashes in the morning in south and west Wales.
Two people were taken to hospital after a crash between two cars and a lorry on the eastbound A48 near Maesybont, Carmarthenshire, at 0900 GMT.
A man was also taken to hospital after a collision on Caerphilly Road, Cardiff involving two cars just before 0800 GMT.
Other incidents included crashes on the A4055 near Dinas Powys, the A468 Caerphilly road at Bassaleg, Newport and the A4119 Llantrisant Road in Danescourt, Cardiff.
Meanwhile, Rhondda Cynon Taf council closed Bwlch, Maerdy and Rhigos mountain roads overnight on Monday as a precaution.
Anyone in the Rhondda experiencing persistent problems with their water supply should contact Welsh Water on 0800 052 0130.