How do ice cubes make the whole drink cold?

As water cools below 40F, it's density starts to decrease (which is anomalous, normally there is a density increase going from liquid to solid). This results in the ice being less dense than the surrounding liquid (thus the ice floats). While floating the ice cools the liquid that comes in contact with it (presumably warmer than 40F). This makes the liquid more dense than the surrounding liquid, making it drop to the bottom of the glass. And, subsequently is replaced by more warm liquid. As this process is continued, your entire drink gets cold.