Australia is believed to have between 400,000 and one million brumbies, making up the largest population of wild horses in the world.
Known for their intelligence and calm temperament, they have survived in vastly different landscapes, including the Outback and bushland.
They were deployed as cavalry mounts in the Boer War and World War I and II.
But the brumbies of the Snowy Mountains have developed a near-mythical status, particularly since featuring in The Man From Snowy River, a famous 19th century poem by Banjo Paterson which was adapted into a 1982 movie starring Kirk Douglas.
Save the Brumbies, an organisation which supports Australians keeping the horses domestically, said the proposal to shoot thousands of animals from the ground was "absolutely horrific".
"They are our culture, they are an icon and they deserve to have protection and above all they deserve to have humane handling," Jan Carter, the organisation's president, told ABC News.
"We have independent reports... that they do not cause the damage that they are accused of."
A plan outlining the cull was released at the weekend and will be open to public submissions until July 8.
Numerous culls have been conducted across Australia in recent years and have often provoked angry public responses. In New South Wales, aerial shooting was banned after 600 horses were shot in 2000 in a three-day cull.
Most scientists and conservationists have supported humane and limited culls of brumbies, saying they cause serious damage to vegetation.
Dr Graeme Worboys, from the International Union for Conservation of Nature, argued last year that the brumbies should be removed from parks where authorities were trying to protect native species.
"They compact the wetlands, they pug the marshy areas, they destroy the stream banks and cause erosion," he said.
