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Southern District Command Centre deployment co-ordinator Senior Sergeant Matt Scoles said the driver of the Trail Journeys van was flown to Dunedin Hospital with a serious arm injury.
The van flipped on State Highway 87 between Mosgiel and Middlemarch about 9am.
The man was to have surgery on his arm yesterday afternoon, Snr Sgt Scoles said.
He was in a stable condition in a general ward last night.
A St John spokesman said the three passengers had minor or no injuries and were treated at the scene, on Sutton-Clarks Junction Rd.
Mark Fraser, of Mosgiel, said he arrived at the scene moments after the crash.
The three passengers were stuck, and the driver's arm was pinned under the van, which was on its side.
The passengers escaped through the windscreen, which he and another motorist helped remove. It had been cracked in the crash.
The first motorist had alerted the emergency services.
The driver's right arm was pinned under the vehicle. Mr Fraser said they considered jacking up the vehicle, but were advised not to by emergency services.
''He was in a lot of pain ... it was starting to tingle.''
The driver stayed calm throughout the ordeal, Mr Fraser said.
When emergency services, including the Otago Regional Rescue Helicopter, arrived, the two men helped lift the van off the driver.
Mr Fraser said he had been travelling at 60kmh for up to 10km before the crash, because of black ice.
Passenger Ellen McLean (20), a Dunedin student, said she had only a ''little scratch'' and counted herself very lucky.
She was looking at her phone when the van started to skid. It flipped on to its side. The passengers tried to open the van's sliding door but could not.
None of the passengers panicked: ''We were all just a bit stunned.''
The driver asked if everyone was all right, before telling passengers his arm was stuck.
Mt Gowrie Station owner Ainslie McDonald said she was cooking scones in the homestead when she saw the emergency services arrive.
Her husband Jim, a former ambulance officer, and youngest son Heath, helped the emergency service staff.
An overnight snow flurry had frozen and made surfaces greasy, she said.
''Both my husband and son fell over this morning when opening gates to feed stock. It was very, very dicey. The conditions weren't flash at all.''
A Trail Journeys spokeswoman declined to comment when the ODT contacted the Clyde office yesterday.
The Trail Journeys website said the company provided daily door-to-door Dunedin-to-Cromwell return trips with its Catch A Bus service.
NZTA maintenance contract manager Nick Rodger said the highway was patrolled earlier in the morning and deemed ''fine'' and no grit was required but ice formed on it by 8.30am.
''We had very little warning. It was a very late frost and we had no indication it was going to freeze.''