About 2.6 million years ago the Antarctic polar cap was formed as the Earth entered the current ice age, rapidly growing to cover the entire continent. In the intervening time the ice has increased for spans of ~100,000 years during glacial periods and decreased for spans of ~20,000 years during interglacial periods such as the Holocene interglacial we are currently in. According to ice core data this has happened five times in the last 500,000 years.
In a span of time beginning about 18,000 years ago and ending about 0 CE polar ice was melting at such a high rate that global sea levels rose 130 meters as the climate warmed. The climate then switched to cooling again, the poles accumulating enough ice to lower sea levels by 10 meters in about 1800 years. About the beginning of the Industrial era the ice began melting again.
The total ice amount in volume or gigatons is important because the phase change of water requires huge amounts of energy, which reflects changes in the thermal equilibrium of the planet - net warming or cooling is measured in gigatons of ice. On this measure globally the net ice is currently decreasing, but proportionally on a scale that would lead to a total loss of polar ice on the order of a million years. We need to keep a close eye on this, as human activity appears to be impacting the thermal balance and continuing to do so could accelerate that change significantly.
So that is net ice for both poles. At the north pole sea ice is reducing in extent and thickness, resulting in more exposed ocean. In the southern ocean sea ice is increasing in extent as sea level rise and warmer seas accelerate flows of land ice onto the sea, and glacial runoff freezes more readily than sea water. In addition to the impacts on sea life and human activities these changes can affect global thermal energy flows. Sea ice is highly reflective of solar energy, reflecting sunlight back into space and impacting the thermal balance also.
It is all quite complex, but these are the climate issues we need to keep an eye on. Rising CO2 causes rising surface air temperatures, which impacts ocean temperatures over time, but it is the vast thermal energy sink of frozen water that moderates the climate temperature overall. The ice in your beverage maintains its temperature at a constant while it is present, and once it is gone then rapid changes can occur. The insulation properties of your cup affect the energy flows, and so, how fast the ice melts.