The Antarctic Treaty (and subsequent treaties) forbid colonization. They also forbid extraction of useful resources from Antarctica, thereby eliminating one of the main motivations for colonization. They further forbid any profitable capitalist activity on the continent. So you can’t even do activities that would tend toward permanent settlement, like surveying to find mining opportunities, or opening a tourist hotel. Basically, the treaty system is set up so that not only can’t you colonize, but you can’t even get close to colonizi... (read more)
We arguably have already colonized Antarctica. See Wikipedia.
A similar point would be: There is no permanent deep sea settlement (an underwater habitat), although this would be much easier to achieve than a settlement on Mars.
4JBlack
In principle I suppose one could build very large walls around it to reduce heat exchange with the rest of Earth and a statite mirror (or few slowly orbiting ones) to warm it up. That would change the southern hemisphere circulation patterns somewhat, but could be arranged to not affect the overall heat balance of the rest of Earth.
This is very unlikely to happen for any number of good reasons.