The Firefox UI is heavily dependent on CSS. You can tweak that CSS if you're so inclined.

1. Create a userChrome.css file
2. Inspect the Firefox UI using Firefox's own "Remote Debugger"
3. Write your styles in userChrome.css
4. Restart Firefox to apply your changes

Sample styles

Note: Waterfox, a fork of Firefox, has built-in settings to disable the bookmark toolbar icons and labels, which was my original motivation for writing this HOWTO.

Hide the favicons:

.bookmark-item > image.toolbarbutton-icon {
    display: none;
}

Hide labels for non-folder buttons:

.bookmark-item:not([container="true"]) > label.toolbarbutton-text {
    display: none !important;
}

Screenshot