exclude-tag-from-tag-cloud.php

<?php

add_filter( 'widget_tag_cloud_args', 'jmw_exclude_tag_from_tag_cloud');
function jmw_exclude_tag_from_tag_cloud( $args ) {
  $args[ 'exclude' ] = '36'; // ID of the tag. If multiple tags use comma delimited sting '2,5,36'
  return $args;
}

/* 
* Other arguments that can be changed
* 'smallest'                  => 8, 
* 'largest'                   => 22,
* 'unit'                      => 'pt', 
* 'number'                    => 45,  
* 'format'                    => 'flat',
* 'separator'                 => "\n",
* 'orderby'                   => 'name', 
* 'order'                     => 'ASC',
* 'exclude'                   => null, 
* 'include'                   => null, 
* 'topic_count_text_callback' => default_topic_count_text,
* 'link'                      => 'view', 
* 'taxonomy'                  => 'post_tag', 
* 'echo'                      => true,
*/