Constable Steve Wykes, of Dunedin, said a car slid off State Highway 87 in Woodside, west of Outram, about noon.
Two men were in the Nissan Tiida car when it crashed, near Woodside Rd.
Both men were international students who were living in the North Island.
The stretch of highway was ``a little icy'' and had been gritted, Const Wykes said.
The car slid from the highway on a sweeping bend and travelled about 25m down a bank.
The driver was travelling within the 100kmh speed limit but the ``ice, speed and grit had contributed'' to the crash.
``Drive to the conditions, even when the road has been gritted - watch that speed.''
St John spokesman Gerard Campbell said an ambulance was deployed and the two men were treated at the scene.
MetService meteorologist Ciaran Doolin said the -4.8degC recorded in Middlemarch about 9am made it the coldest place in Dunedin yesterday.
The town was the second-coldest place in Otago yesterday, warmer only than the -5.1degC recorded in Ranfurly about 5am.
