Supt Tim Swarbrick said: "It's a tragedy at this time of the year and our thoughts are with the families of all those involved."
The Chief Executive of the South Western Ambulance Service Trust, Ken Wenman, praised everyone involved in the rescue operation.
He said: "The effective response from emergency services, combined with the local community's willingness to help, resulted in the delivery of high quality care to a large number of patients in very challenging circumstances."
The injured bus passengers were taken to Treliske Hospital in Truro after the crash.
'Difficult to breathe'
A police spokesman said one of the women killed was pronounced dead at the scene. The other is believed to have died after being taken to hospital.
Police said the women were from the west Cornwall area and their families have been informed.
The operations manager at Camborne-based Williams Travel, Garry Williams, said: "I attended Treliske Hospital to speak to the driver and a number of passengers, all of which said that the coach was unable to stop once it had come into contact with the black ice, and then turned over onto its side and ended up in a ditch.
"All were amazed that this road was not gritted, which is a regular road used by those who go to see the Christmas lights.
"Our thoughts are with the families and friends of those passengers who sadly died, and also all the other passengers who were on the coach."
The regional engineer with Cornwall County Highways, Peter Tatlow, said: "It's one of the more minor roads so therefore it wouldn't have been treated as a matter of course."
Of the 47 people hurt, four are described as seriously injured and the rest are "walking wounded".
At 1400 GMT Police confirmed three people were still in hospital.
The crashed police car has been removed and diggers are attempting to clear the ground around the bus.
Police hope to recover the vehicle later.
Derek Smith lives near the site of the crash and went to help
The coach left the road as it went down a hill, hit a tree and ploughed through a hedge before coming to a stop on its side, Devon and Cornwall Police said.
Insp Matt Shaw said: "It seems from initial investigations that the coach has slipped on ice. The road is covered in a sheet of ice, it's treacherous, it's difficult to even walk down there."
The operation involved the police, firefighters, coastguards and Cornwall's specialist search and rescue team.
During the morning, up to 20 police officers remained at the scene, about seven miles north-east of Penzance, and crash scene investigators were at work.
Helicopters from RNAS Culdrose near Helston and RMB Chivenor were sent to help take casualties to hospital in Truro because the roads were too treacherous, police said.
It took four hours to move all the injured passengers to hospital.
The atrocious weather has caused several other collisions in Cornwall.
Part of the A30 was closed at Bodmin after black ice caused a collision between a heavy goods vehicle and two cars.
There were also accidents on both sides of the A38 - one in Liskeard and another on the Dobwalls bypass.
Coach passenger Ann Ellis said she was ''shaken'' after the crash in Cornwall
Some buses have been cancelled as was the 0740 train from Penzance to Paddington. Passengers are being warned the cancellation will affect trains later in the day.
Truro's Park and Ride service was closed because of ice but has now re-opened.
The Royal Cornwall Hospital is advising patients due to attend routine outpatient or non-urgent appointments to consider their personal safety before setting out.
The trust said: "If they feel it is unsafe to travel they should not worry as we will be able to offer them another appointment at a later date.
"Our clinics are operating as normal but it would be helpful if patients could telephone in the event they are unable to attend."
Police are advising people to stay off the roads unless their journeys are absolutely necessary.
Forecasters said the temperatures in Cornwall on Tuesday night would have been as low as -1C (30F) but could have been lower in isolated spots.
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