No, snow leopards don’t live in Antartica. They live thousands of miles from Antarctica as the map below shows you.
Think of the high plains of the Plateau of Tibet and the cold mountains of Mongolia. These are the sort of places where they live. These are wide open, vast areas where humans are unlikely to see them. They do come into contact with farmers though.
Snow leopards are currently in the following countries:
Afghanistan; Bhutan; Tibet; China (Yunnan, Qinghai, Sichuan, Gansu, Xinjiang, Nei Mongol); India (Himachal Pradesh, Sikkim, Jammu-Kashmir, Uttaranchal, Arunachal Pradesh); Kazakhstan; Kyrgyzstan; Mongolia; Nepal; Pakistan; Russian Federation; Tajikistan; Uzbekistan.
The range of the snow leopard extends from the Himalaya in the south, across the Qinghai-Tibet Plateau and the mountains of Central Asia to the mountains of southern Siberia in the north – IUCN Red List
Note: I have deliberately separated Tibet from China unlike the IUCN Red List which assumes that Tibet is part of China. I don’t think it is established. It is in dispute.