This is kind of a strawman argument, really. The ONLY reason Antarctica has not been mined and otherwise exploited is because of an international agreement prohibiting that very activity. It's not because it's so technically difficult.
That said, there are large portions of Antarctica where it IS technically difficult, and I would argue that prospecting and mining through a couple of miles of solid, moving ice is actually more difficult than doing so through a hundred million miles, more or less, of empty space.
I'm not sure about that.
I suspect that while mining in Antarctica is technically feasible, it is very expensive compared to mining on other continents, and until we've mined out those other places there is no real need to mine Antarctica. I further suspect that if this was not the case, all the treaty stuff would go out the window pretty fast. It's very easy to do the right thing when it is cheaper and easier than doing the wrong thing.