A significant amount of snow on the ground slightly absorbs and dampens sounds, as IrateAnteater says, similar to being in an anechoic chamber.

Significant rain or sleet or hail causes its own background noise that can functionally mask other background sounds... and, if an area with roads is now very wet, this changes the sound of cars driving nearby to be a bit more ... treble, high pitched, as the water splashing out of the way is now part of your average car driving by sound... and basically, close by sounds that are now higher pitched are more noticeable.

Differing levels of temperature, atmospheric pressure and humidity also alter how sound propogates through the air.

https://www.researchgate.net/publication/289525229_Influence_of_Atmospheric_Conditions_on_Sound_Propagation_-_Mathematical_Modeling

The effects are most noticable for sounds that are basically in the 'background noise' category; certain weather conditions can be the difference between you being able to mostly hear them, and mostly not hear them.