In the case of the ice in the Antarctic this isn't really true. As dmcee commented on joshphysics' answer, what happens when water freezes under normal circumstances is that the entropy of the water itself drops as it becomes ice, but at the same time heat is released, and this increases the entropy of the surroundings. So the total entropy increases, but the entropy of the ice is still lower than the surrounding water. In thermodynamics, when we talk about the entropy of a system, we always mean just the entropy that's inside the system, not including the entropy of its environment. The only exception to this is when we say "entropy always increases", in which case we do mean the total entropy!
However, it is possible for ice to have a higher entropy than water under some circumstances. If you take very pure water and cool it very carefully, it is possible for it to become supercooled, as in this video. Supercooled water stays liquid even though it's below its freezing point, but if you shake it or add a small particle of dust then ice crystals will form. This will happen even if the supercooled water is in an insulated container, so that it cannot increase the entropy of its surroundings by heating them up. In this case heat is still released, but it just increases the temperature of the system. So the ice that forms is slightly warmer than the supercooled water that it comes from, but it's still below the freezing point. Since this is a spontaneous process taking place in an isolated system, it must increase the entropy, and so we can conclude that the solid ice has a higher entropy than the liquid supercooled water.