Cooney, who is in his early 50s, regained consciousness before being taken to hospital, where he was joined by his wife and daughter.
Last night, Auckland Trotting Club chief executive Graeme Running said Cooney was a respected and much-liked driver and trainer.
The racing community would be shocked by the accident, but would quickly rally and offer support.
"What ends up happening in a situation like this is the racing community pulls together pretty well and looks after one another."
Cooney is an Alexandra Park regular and has driven more than 600 winners.
Mr Running, who was not at the track last night, said Cooney was an old hand who "knew the ropes".
Such a serious crash in harness racing was extremely rare, he said.
The last serious racing accident at Alexandra Park from which a driver was taken to hospital was in March 2008, when Tony Shaw suffered serious head injuries after he was catapulted from his sulky.
He was put into an induced coma on life support after an operation which released fluid from his brain.
He had three months of rehabilitation and though he has returned to the sport, his driving career ended.
"[Given] the number of times the track and training track and everything gets used with horses, it's very rare there are any bad accidents," Mr Running said.
Harness Racing New Zealand chief executive Edward Rennell said stipendiary stewards would investigate the incident to determine what went wrong.
The investigation would look at other drivers' and horses' behaviour.
"Obviously our thoughts at the moment are with the driver and his family," said Mr Rennell.