The Xclear extension () installs a "clear" button to the end of the awesomebar/urlbar, findbar, and the search field.
It was created for Linux users who "don't want their clipboards to be erased when marking the text in the field to delete it." (author's words, not mine)

This userstyle was written so that nobody is required to modify their userChrome.css file.
One click from the Stylish menu, and you're good to go.

It also makes the icon hidden until hovered over, so that it's only visible when you are about to click on it.

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All credit goes to the author of the add-on, Peter Leugner () for the extension, and his userChrome.css modifications from the add-on page.

(Seriously, go look at the add-on page - his code is right there when you hit the Page Down key.)