TinyMCE, show character count instead of word count

Write your own plugin.

The following solution is based on this article. The charactercount plugin counts the actual characters that the user sees, all HTML and hidden characters are ignored. The number is updated on every "key up" event.

Character Count Plugin:

tinymce.PluginManager.add('charactercount', function (editor) {
  var self = this;

  function update() {
    editor.theme.panel.find('#charactercount').text(['Characters: {0}', self.getCount()]);
  }

  editor.on('init', function () {
    var statusbar = editor.theme.panel && editor.theme.panel.find('#statusbar')[0];

    if (statusbar) {
      window.setTimeout(function () {
        statusbar.insert({
          type: 'label',
          name: 'charactercount',
          text: ['Characters: {0}', self.getCount()],
          classes: 'charactercount',
          disabled: editor.settings.readonly
        }, 0);

        editor.on('setcontent beforeaddundo', update);

        editor.on('keyup', function (e) {
            update();
        });
      }, 0);
    }
  });

  self.getCount = function () {
    var tx = editor.getContent({ format: 'raw' });
    var decoded = decodeHtml(tx);
    // here we strip all HTML tags
    var decodedStripped = decoded.replace(/(<([^>]+)>)/ig, "").trim();
    var tc = decodedStripped.length;
    return tc;
  };

  function decodeHtml(html) {
    var txt = document.createElement("textarea");
    txt.innerHTML = html;
    return txt.value;
  }
});

CSS Tweaks:

/* Optional: Adjust the positioning of the character count text. */
label.mce-charactercount {
  margin: 2px 0 2px 2px;
  padding: 8px;
}

/* Optional: Remove the html path code from the status bar. */
.mce-path {
  display: none !important;
}

TinyMCE Initialization (using jQuery)

$('textarea.tinymce').tinymce({
  plugins: "charactercount",
  statusbar: true,
  init_instance_callback: function (editor) {
    $('.mce-tinymce').show('fast');
    $(editor.getContainer()).find(".mce-path").css("display", "none");
  }
  // ...
});

ps. Use JS minifier.