Add a icon on top of the video by creating a youtube.png image and putting it in a 'images' folder in your theme.

YouTubeWidget.php

<?php
/**
 * Plugin Name: YouTube Video Widget
 * Plugin URI: http://halgatewood.com/
 * Description: Awesome YouTube Widget that allows single videos or latest video from channel. Uses transient api to keep it quick.
 * Author: Hal Gatewood
 * Author URI: http://halgatewood.com/
 * Version: 1.0
 * License: GPL v2 - http://www.gnu.org/licenses/old-licenses/gpl-2.0.html
 * 
 *  CSS AT BOTTOM OF GIST
 * 
 */
 
class YouTubeWidget extends WP_Widget
{
  function YouTubeWidget()
  {
    $widget_ops = array('classname' => 'YouTubeWidget', 'description' => 'Add a YouTube Video to the sidebar' );
    $this->WP_Widget('YouTubeWidget', 'YouTube Video', $widget_ops);
  }
 
  function form($instance)
  {
    $instance = wp_parse_args( (array) $instance, array( 'title' => 'Watch our Video', 'youtube_url' => '' ) );
    $title = $instance['title'];
    $youtube_url = $instance['youtube_url'];
    $youtube_channel = $instance['youtube_channel'];
?>
  
  <p>
    <label for="<?php echo $this->get_field_id('youtube_channel'); ?>">
  		YouTube Username:
  		<input class="widefat" id="<?php echo $this->get_field_id('youtube_channel'); ?>" name="<?php echo $this->get_field_name('youtube_channel'); ?>" type="text" value="<?php echo attribute_escape($youtube_channel); ?>" />
  		<small>(pulls in latest video)</small>
  	</label>
  </p>

  <p>
  	<label for="<?php echo $this->get_field_id('youtube_url'); ?>">
  		Specific YouTube Video URL:
  		<input class="widefat" id="<?php echo $this->get_field_id('youtube_url'); ?>" name="<?php echo $this->get_field_name('youtube_url'); ?>" type="text" value="<?php echo attribute_escape($youtube_url); ?>" />
  		<small>(override latest and use specific video)</small>
  	</label>
  </p>
  
  <p>
  	<label for="<?php echo $this->get_field_id('title'); ?>">
  		Override Title: 
  		<input class="widefat" id="<?php echo $this->get_field_id('title'); ?>" name="<?php echo $this->get_field_name('title'); ?>" type="text" value="<?php echo attribute_escape($title); ?>" />
  	</label>
  </p>
  
<?php
  } // end form function
 
  function update($new_instance, $old_instance)
  {
    $instance = $old_instance;
    $instance['title'] 	= $new_instance['title'];
    $instance['youtube_url'] 		= $new_instance['youtube_url'];
    $instance['youtube_channel'] 	= $new_instance['youtube_channel'];
    return $instance;
  }
  
	function getYouTubeIdFromURL($url) 
	{
		$pattern = '/(?:youtube\.com\/(?:[^\/]+\/.+\/|(?:v|e(?:mbed)?)\/|.*[?&]v=)|youtu\.be\/)([^"&?\/ ]{11})/i';
		preg_match($pattern, $url, $matches);
		
		return isset($matches[1]) ? $matches[1] : false;
	}
 
  function widget($args, $instance)
  {
    extract($args, EXTR_SKIP);
    
    $video_url = "";
    
    if($instance['youtube_channel'])
    {	
    	$transient_name = 'latest_video_' . $youtube_channel;
    	$youtube_channel = $instance['youtube_channel'];
    	
		if( get_transient( $transient_name ) )
	  	{
			$video_data = get_transient( $transient_name );
	    	$video_url		= $video_data['url'];
	    	$video_title 	= $video_data['title'];
		}
		else
		{
	    	$json = json_decode( file_get_contents( "http://gdata.youtube.com/feeds/api/users/" . $youtube_channel . "/uploads?v=2&alt=jsonc" ) );
	    	$user_videos = $json->data->items;
	    	
	    	if($user_videos[0])
	    	{
	    		$latest_video 	= $user_videos[0];
	    		$video_url		= "http://www.youtube.com/watch?v=" . $latest_video->id;
	    		$video_title 	= $latest_video->title;
    		}
    		
    		$transient_data = array( 'url' => $video_url, 'title' => $video_title );
			set_transient( $transient_name, $transient_data, 3600 );
		}
    }
    else
    {
    	$video_url = $instance['youtube_url'];
    }

    if(empty($video_url)) { return; } // NO VIDEO URL, RETURN NOTHING
    $title = empty($instance['title']) ? $video_title : apply_filters('youtube_widget_title', $instance['title']);
    $youtube_id = $this->getYouTubeIdFromURL( $video_url );
	?>
		<li id="<?php echo $widget_id; ?>" class="youtube widget">
			<?php if ( $title ) echo $before_title . $title . $after_title; ?>
			<div class="video">
				<a href="http://www.youtube.com/embed/<?php echo $youtube_id; ?>?rel=0&amp;wmode=transparent&amp;autoplay=1" class="fancybox youtube iframe"><img class="thumbnail" src="http://img.youtube.com/vi/<?php echo $youtube_id; ?>/hqdefault.jpg" /></a>
				<a href="http://www.youtube.com/embed/<?php echo $youtube_id; ?>?rel=0&amp;wmode=transparent&amp;autoplay=1" class="fancybox youtube iframe"><img class="play" src="<?php echo get_template_directory_uri(); ?>/images/youtube.png" alt="" /></a>
			</div>
			
			<script> 
				jQuery(document).ready(function () 
				{  
					jQuery('a.fancybox.youtube').colorbox({iframe:true, innerWidth:640, innerHeight:390});
				});
        	</script>
		</li>
	<?php 
  }
}
add_action( 'widgets_init', create_function('', 'return register_widget("YouTubeWidget");') );


/*

ADD THIS CSS

.youtube.widget .video { position: relative; padding: 0 20px 20px 20px; }
.youtube.widget .video img.thumbnail { width: 100%; height: auto; }
.youtube.widget .video img.play {
	position: absolute;
	width: 72px;
	height: 72px;
	left: 50%;
	top: 50%;
	z-index: 10;
	margin-top: -36px;
	margin-left: -36px;
	opacity: 0.75;
	transition: opacity 0.35s;
	-moz-transition: opacity 0.35s;
	-webkit-transition: opacity 0.35s;
	-o-transition: opacity 0.35s;
}
.youtube.widget .video img.play:hover, 
.youtube.widget .video:hover img.play { opacity: 1; }
*/