Cotton is light and fluffy -- it is mostly air already! But cotton also
has lots of tiny fibers which are tangled up. These fibers keep air
from flowing freely through the cotton.
When ice melts in air, cold air sinks and warm air rises to take
its place because cold air is more dense than warm air (stuff shrinks
when it gets cold, even air!). This constant circulation of warm and
cold air brings new batches of warm air in contact with the ice,
allowing a faster heat transfer to the ice (the heat transfer rate is
proportional to the difference in temperatures of the hot and cold
objects - in this case, air and ice).
In the case with cotton, the air cannot flow, and the air trapped
inside the cotton near the ice becomes as cold as the ice is and stays
put. New hot air cannot replace it to melt the ice faster, and the ice
stays cold longer.
The cotton may get wet, and there will still be some heat flow through it, so the ice will eventually melt.
(republished on 07/25/06)