Updated to WYSIJA Version 2.4, edits wysija-newsletters/controllers/front/email.php to allow only logged in users to see HTML version of newsletter.

email.php

<?php
defined('WYSIJA') or die('Restricted access');

include_once( ABSPATH . "wp-includes/pluggable.php");
global $current_user;

class WYSIJA_control_front_email extends WYSIJA_control_front{
    var $model='email';
    var $view='email';

    function WYSIJA_control_front_email(){
        parent::WYSIJA_control_front();
    }

    function view(){

        if( is_user_logged_in() ) {

        $data=array();

        header('Content-type:text/html; charset=utf-8');

        // Get email model as object.
        $emailM =& WYSIJA::get('email','model');
        $emailM->getFormat = OBJECT;
        // Get config model
        $configM =& WYSIJA::get('config','model');

        // Helpers
        $emailH =& WYSIJA::get('email','helper');
        $mailerH =& WYSIJA::get('mailer','helper');

        // Get current email object.
        $current_email = $emailM->getOne((int)$_REQUEST['email_id']);

        // Get current user object if possible
        $current_user = null;
        if(isset($_REQUEST['user_id'])){
            // Get User Model
            $userM = &WYSIJA::get('user','model');
            $userM->getFormat = OBJECT;
            $current_user = $userM->getOne((int)$_REQUEST['user_id']);
        }

        // Parse and replace user tags.
        $mailerH->parseUserTags($current_email);
        $mailerH->parseSubjectUserTags($current_email);
        $mailerH->replaceusertags($current_email, $current_user);

        // Parse and replace old shortcodes.
        // $emailObject->subject = str_replace(
        //         array('[total]','[number]','[post_title]'),
        //         array($itemCount, $totalCount, $firstSubject),
        //         $emailChild['subject']);

        // Set Body
        $email_render = $current_email->body;

        // Parse old shortcodes that we are parsing in the queue.
        $find = array(
            '[unsubscribe_linklabel]',
            '[post_title]',
            '[total]',
            '[number]'
        );
        $replace = array(
            $configM->getValue('unsubscribe_linkname'),
            $current_email->params['autonl']['articles']['first_subject'],
            $current_email->params['autonl']['articles']['total'],
            $current_email->params['autonl']['articles']['ids']
        );
        $email_render = str_replace($find, $replace, $email_render);

        // Strip unsubscribe links.
        $email_render = $emailH->stripPersonalLinks($email_render);

        do_action( 'wysija_preview', array(&$this));

        echo $email_render;

        exit;

        }

        else {
        //echo "<p>This content available only to authorized users.</p>";
        global $wp_query;
        header("HTTP/1.0 404 Not Found - Archive Empty");
        $wp_query->set_404();
        require get_stylesheet_directory().'/404.php';
        exit;
        }

    }

}