How to remove hide the select arrow in Firefox using
-moz-appearance:none;

More info and background:

Check this cheesy gist for the full story.

It's as hacky simple as:

  1. Set
    -prefix-appearance
    to none to remove the styles;
  2. Use
    text-indent
    to "push" the content a bit to the right;
  3. Finally, set
    text-overflow
    to an empty string. Everything that extends beyond it's width will become... nothing! And that includes the arrow.

Brought to you by @joaocunha

Follow the guy!