The IPCC says (PDF page 4, report page 656 of an older report):
Increased melting of Arctic glaciers and the Greenland ice sheet, but thickening of the Antarctic ice sheet due to increased precipitation, were projected.
- Climate change is leading to increased precipitation. (Short version: Warm air picks up more humidity.) In places where it is cold enough, that precipitation is snow/ice.
- The Antarctic is significantly colder than the Arctic--because land can get colder than water in the first place and also because it has higher elevations. In this case, the Antarctic is cold enough that it doesn't melt so much, whereas the Arctic is warmer and melts more.
- Once it gets warm and starts melting, melting (and rain) makes local temperatures warmer and leads to more melting, but snow makes local temperatures colder, i.e. less melting (short version: liquid surface water makes ice which is dark-colored and radiates sunlight as heat, snow is light-colored and radiates sunlight as light).
This doesn't mean that the Antarctic is safe forever, if the global temperatures increase enough then even a locally colder temperature won't be cold enough to prevent melting...and once melting starts, it can create a feedback loop which increases the speed of melting.
You can see this kind of local variation within Antarctica as well. East Antarctica is higher (and colder, for reasons above) than West Antarctica --and the eastern side has been (slightly) gaining ice while the western side has been losing ice.