About 40 of the animals had already died from dehydration and starvation. Surviving horses were later culled, the CLC added.
Another 120 feral horses, donkeys and camels "dying from thirst" will also be culled in a neighbouring community, CLC Director David Ross told the BBC.
Temperatures in Alice Springs have exceeded 42 degrees Celsius for almost two weeks - more than 6 degrees above January's average, according to the Australia's Bureau of Meteorology.
The extreme weather follows the record-breaking heatwave that produced five of Australia's 10 warmest days on record.
Several other wildlife species have also suffered, including reports of mass deaths of native bats in New South Wales.
Up to a million fish have been found dead along river banks in the drought-affected state.