For some reason all the other geeklets that claim to display the weather and weather icon on your desktop never worked for me. After some searching I finally found this. It isn't my work, I'm just sharing.
First download "Weather (info)" and add it as a shell. This command retrieves the weather icon from Yahoo! and stores it as a temporary file on your computer. I set the refresh rate to 300 seconds (5 minutes) because I didn't want it constantly looking online for new icons. NOTE: THE ICON WILL NOT SHOW UP ONCE YOU SET UP THIS SHELL, HOWEVER IT MUST REMAIN ON YOUR DESKTOP OR ELSE THE NEXT STEP WON'T WORK.
Second, download "Weather (image)" and add it as an image. This command will take the temporary image you downloaded using the shell from step one, and display it as an image on your desktop. Again, I set the refresh rate to 300 seconds.
Finally, download the "Weather (description)" file and add it as a shell. This will add a short description of the current weather outside (such as "Partly Cloudy, 67F"). I also used 300 seconds as my refresh rate and you can edit the font, size and color as you see fit.
NOTE: The files are configured to retreive the weather for Storrs, CT. To change the weather for your town, you must follow a couple steps.
First, to change the weather icon, simply go to Yahoo! Weather and go to the main weather page for your area. Copy the URL and paste it in the shell command area, (from Weather (info)) replacing the URL for Storrs, CT (http://weather.yahoo.com/united-states/connecticut/storrs-12760328/)
Second, to change the weather description, you must click the "RSS" button on the same weather page you were just on. It's located near the top right of the page and is in orange. It will bring you to another page where you can copy the URL and paste it over the shell for "Weather (description)", replacing the information for Storrs, CT (http://weather.yahooapis.com/forecastrss?p=USCT0222&u=f).
After both of these steps you should be all set.
One final thing, when you first start up your computer or first install these shells, the icons or information may not appear right away. Simply click on the GeekTool icon in the menu bar and click "refresh all".