If you are hearing rain sounds during, for example, the extra sunny, clear and/or overcast weathers, your weather.xml file is most likely modified. To fix this and no longer hear rain sounds during weathers where no rain should be present, navigate (using OpenIV or a similar program) to:
mods > update > update.rpf > common > data > levels > gta5
and edit weather.xml.
In weather.xml, find "<WeatherTypes>". For each weather type (which is noted by its respective name in the weather.xml file) you wish to remove the rain sound , find the "Rain" subelement. If the value of the rain is higher than 0, you will hear the rain sound and may see raindrops when it is that weather in-game. To disable the rain sound, edit the element to:
<Rain value="0.000000"/>
Click save.
Now, whenever it is that weather in-game, you will no longer hear the rain sound!