Sound does not actually increase in amplitude, or loudness, in the cold. However, two factors come together and make people perceive sound as much louder in the cold: the cold itself and the snow that often comes with it.
The primary factor that makes people perceive sound as louder in the cold is the temperature itself. The speed of sound becomes slower as temperatures drop, which means that people perceive sound for slightly longer periods of time in the cold, and that longer period of perception is often perceived as loudness. A smaller factor that sometimes makes people perceive sound as louder in the cold is snow. Porous blankets of snow tend to absorb sound waves. While this dampens local background noises, it can, as a result, enhance the perception of loud noises, like airplane takeoffs, at a distance.