The basic understanding of ocean currents is that warm currents carry moisture whereas cold currents carry nutrients. This is why some scientists believe in the connection between the Arctic ice caps and the warm Gulf Stream and the frigid Humboldt and Benguela currents turning the tropical lands of Chile and Namibia bone-dry.
With that, there are some confusions with the workings of coldwater ocean currents. Antarctica is surrounded by the Antarctic Circumpolar Current, a coldwater current, yet it is covered in mile after mile of frozen water. The Pacific coast of North America is nurtured by coldwater currents, yet we see temperate rainforests.
So what's going on? Why are there habitats that require a lot of moisture near coldwater ocean currents that can't carry that much?