In general, substances decrease in size on cooling as cooling decreases the average kinetic energy of the system, reducing the extent that the particles comprising the substance can overcome the intermolecular forces present that hold the particles together.
It is for this reason that many substances become more dense as temperature decreases. For example, cold air (which is technically a mixture, but it works for our purposes) is denser than warm air, and cold water is denser than warm water. Density is defined as the amount of mass per volume. If the temperature is reduced, the amount of mass isn’t changed. So the increase in density must be due to the change in volume; for density to go up, the volume must go down. One can consider this in isolation: a balloon placed in a freezer will shrivel up as the “size” of the gas inside the balloon decreases.
There are, of course, exceptions, the most famous perhaps being water. While water, like most liquids, does decrease in size on cooling, it only does so up to a point (specifically 4 degrees C); after this point, water expands (its volume increases and density decreases) as it is cooled further, which holds even after it freezes; that is why solid water (ice) floats in liquid water—which isn’t the case with many other substances whose solids states are denser than their liquid states.
