Log into server via shell:
vi /usr/local/cpanel/base/horde/imp/config/mime_drivers.php
Look for code batch:
/* HTML driver settings */
'html' => array(
/* NOTE: Inline HTML display is turned OFF by default. */
'inline' => false,
'handles' => array(
'text/html'
),
Change 'inline' => false, to 'inline' => true,
Then run:
/usr/local/cpanel/bin/update_horde_config as root.
Done, all your customers can access emails with HTML output.