Add custom variable in Contact Form 7 mail body

You should do it like so:

add_action( 'wpcf7_init', 'custom_add_form_tag_my_source' );

function custom_add_form_tag_my_source() {
  // "my-source" is the type of the form-tag
  wpcf7_add_form_tag( 'my-source', 'custom_my_source_form_tag_handler' );
}

function custom_my_source_form_tag_handler( $tag ) {
  return isset( $_COOKIE['my_source'] ) ? $_COOKIE['my_source'] : '';
}

See the documentation for more details.

Or you can also try this, to parse regular shortcodes:

add_filter( 'wpcf7_mail_components', function( $components ){
  $components['body'] = do_shortcode( $components['body'] );
  return $components;
} );