You can stay on the ice in scientific stations. Which one depends on the country that runs it ie, New Zealand (Scott Base), USA (McMurdo Base). I know a few people who have been there as scientists but if you are an engineer, cook etc you can also go. You would have to find the relevant base and find out how to get there.....
Getting there's the easy part. The hard part is leaving. The weather down there does not play well with aircraft, and tends to pop up at the least convenient time possible.
Ships go there. Sometimes they get stuck in the ice.
by boat
