Here's why:

* Ideal Gas Law: The Ideal Gas Law states that the pressure (P), volume (V), and temperature (T) of a gas are related by the following equation: PV = nRT, where n is the number of moles of gas and R is the ideal gas constant.

* Density and Temperature: Density is defined as mass per unit volume. For a given mass of air, the density will be higher at lower temperatures. This is because the molecules are moving slower and therefore take up less space.

* Molecular Motion: At lower temperatures, gas molecules have less kinetic energy and therefore move slower. This means they collide less frequently and are more likely to be found in a smaller volume.

In summary: While the number of molecules in a given sample of air remains constant, the density (and thus the number of molecules per unit volume) is higher in cold air due to the slower molecular motion.