The Go Orange charter passengers were returning from a day trip to the skifield when the bus swerved into a snow bank and hit a rock, which forced the bus to jolt violently.
Two helicopters and three ambulances were sent to the scene.
Several people, including a 4-year-old girl, were injured, but most were discharged from Lakes Hospital overnight.
One woman, flown to Dunedin Hospital with slightly more serious injuries, was due to be discharged today.
The Commercial Vehicle Investigation Unit is inspecting the bus for mechanical damage to determine if a vehicle fault might have been the cause.
Police said the vehicle was being removed from the scene today, as poor weather had prevented its removal last night.