Hello there. This issue was also annoying me quite a bit, I've developed a bit of a workaround...
1)If Firefox isn't already, pin it to the task bar
2) Fire up Internet Explorer and Navigate to the page you'd like to have pinned.
3) Right click and hold on the icon to the left of the web address and drag it to the desktop (the icon should display the shortcut with the desired icon)
4) Now is the time to modify the name, if you don't like the one selected.
5) Click and drag the icon to the firefox icon on the task bar
With any luck, it will now appear with the icon.
I've used this with google, weather, facebook and a couple others. all have worked ok.
Hope this helps!