o.k... then another way...
/usr/local/psa/admin/bin/autoinstaller --select-product-id plesk --select-release-current --remove-component horde --remove-component roundcube
/usr/local/psa/admin/sbin/httpdmng --reconfigure-all
service apache2 restart && service nginx restart && service php5-fpm restart
mv /usr/share/psa-roundcube /usr/share/psa-roundcube.backup
mv /usr/share/psa-horde /usr/share/psa-horde.backup
/usr/local/psa/admin/bin/autoinstaller --select-product-id plesk --select-release-current --install-component horde --install-component roundcube
/usr/local/psa/admin/sbin/httpdmng --reconfigure-all
service apache2 restart && service nginx restart && service php5-fpm restart
Check over the Plesk Control Panel, if the desired Webmail ( Horde or Roundcube ) is used in the domain specific mail settings and tryout as well the other webmail feature. When you changed the webmail feature, Plesk should rewrite the configuration files and restart the webserver automatically. Please try out both features and investigate the depending error - logs like you did earlier after you tried to open the webmail URL with the browser. For Horde you should look as well at the logs in "/var/log/psa-horde/"
... and please switch on the psa-firewall again... the issues doesn't seem to be related to it.