"In time they will do anything their owners ask of them, but in the early days they need sympathetic handling to ensure they make a successful transition to domestic life," Haultain said.
"Kaimanawas have an X-factor, their senses are acute and they have proven to be very trainable.
"Given the right environment they are very curious, honest and friendly and are suitable for a variety of equine disciplines."
They have become popular as sport horses, with the reduction in herd numbers improving the horses' condition and their height.
"Ideally all suitable horses will be rehomed, as was the case for the horses mustered in 2016 and 2018," Department of Conservation operations manager Dave Lumley said.
"However, we know it's a real challenge for the rehoming groups to find so many suitable homes."
As many horses as possible will be rehomed, but any deemed medically unfit by a vet will be euthanised under vet supervision.
The rehoming groups can offer support and advice to new owners.
More information and an application form are available online at https://kaimanawaheritagehorses.org/2019-muster/ Applications close on Monday, April 1.