Change the background of the TinyMCE editor with available WP arguments

So this is how I achieved what I was after –

The filter 'tiny_mce_before_init' is used to update the settings of the editor, so you can add your own JS to the 'setup' key.

add_filter('tiny_mce_before_init', 'initiate_tinyMCE_wordcount');
function initiate_tinyMCE_wordcount($initArray){

    $initArray['setup'] = <<<JS
[function(ed){

    ed.onLoad.add(function(ed, e){

        var tb_name = tinyMCE.activeEditor.id; // The ID of the active editor

        /** Check to see if the text editor (not the TinyMCE iframe) has the class 'error' */
        if($('#'+tb_name).hasClass('error')){
            tinyMCE.activeEditor // Thanks fot @Kaiser for this bit
                .getWin()
                .document.body.style.backgroundColor="#FFEBE8";
        }

    });

    return $initArray;

}