After a Plesk upgrade, it’s possible that some services don’t do what they’re supposed to be doing (and have done right, before the update). It could be a Horde Webmail that is displaying a default Plesk page, instead of the webmail-client, or it could be something entirely different.
One of the easiest things to try, and one that solves a lot of Plesk issues, is running the command that will re-configure all services on the server, according to the Plesk internal database. That database contains all settings for mailboxes, DNS-records, web-users, additional settings, …
Here’s how to run it
/usr/local/psa/admin/bin/websrvmng -av
It’s harmless – as your services installed should always be configured with the latest Plesk Database Information (this normally happens automatically).
If that doesn’t do the trick to get Horde Webmail back, you could try reading up on Common Problems With Horde Webmail and Plesk.