I may not have explained it totally right, but the most you can do is change the graphic image itself. If you start renaming them, or re-organizing them, then you could get the wrong image for display, or worse, not get any image at all.
In the case of Xlobby's xweather, or xoapweather, you can look at the xlobby/plugins/xweather/image (or xoapweather/image) directory to see the different image.png files that are used.
Here's an xlobby thread that links to sites where you can download different weather image paks. If you look at them, they are all structured basically the same way.
viewtopic.php?f=7&t=4262 (Ooppss, just checked some of the links and they are now dead, but google weather icons and you can download different packages)
I just googled "weather icons" under "Images" and came up with this template that basically shows what I tried to explain above:

Hope that helps.