Symptoms
A customer opens webmail in CP > Mail > Webmail > open webmail
Webmail is either opening very slow, or fails with timeout error.
Cause
One of the causes might be that there are a lot(15k+) e-mails in the INBOX.
The Horde is designed in a way that it loads the headers of all the mails in the INBOX, and then sorts them before showing to the client.
Resolution
Move some mails from the INBOX to other folder, or move some old mails to trash.