Parts of the park will remain closed for several months during autumn and winter as shooting operations take place to reduce horse numbers, which surged when rehoming was favoured under the previous coalition governments.

Previous counts showed there were more than 20,000 wild horses in the park, government officials have said, posing a risk to the delicate alpine ecosystem.

NSW has a legislated target to cut the brumby population to 3000 by 2027, but the group - which has long campaigned against the culls - is seeking a pause to the shooting.

In its submissions to the court, it argued that aerial shooting without preference for other control methods was "unnecessarily or unjustifiably" inflicting pain upon the horses and was an act of animal cruelty.

The case was briefly back in court for directions on Tuesday, when a motion hearing was set down for June.

The volunteer-run group that launched the action is made up of recreational users of the national park, who say their goals include protecting mountain heritage and traditions, as well as the environment.

Ms Sharpe's choice of aerial shooting to control brumby numbers was based on misleading or inaccurate advice, the group said in its appeal to the court.

It claims that survey data suggested there might have been fewer than 3300 horses in the national park in late February.

The feral horse count in the national park has exploded, according to official counts, since then-NSW Nationals leader and deputy premier John Barilaro opposed culls in favour of trapping and rehoming in 2018.

Some forms of culling were reintroduced in 2021 in an effort to bring the population down to a sustainable figure, but numbers have continued to increase.