No country in the southern hemisphere has ever hosted Winter Olympic Games
Because Winter Olympic Games are usually held in February, a time, when it’s mid-summer in southern hemisphere, most countries that could possibly host the Winter Olympics from southern hemisphere can’t meet the requirements to host them.
There have been few propositions to host Winter Olympic Games in different dates, so it would be possible for countries like Australia, New Zealand, Argentina, Chile and Peru to host the games. Even though International Olympic Committee has declined all suggestions this far, the idea is still open for discussion.