WHM Webmail

WHM Webmail gives two options : Horde or RoundCube to be set as default webmail client.



RoundCube Webmail is a PHP webmail client that will work with a MySQL or Postgres database. One appealing feature it brings is the ability to skin the application-style user interface using XHTML and CSS 2. The app is a multi-language IMAP client whose features include MIME support, address book, editable folder search and spelling check, and it works in your web browser.
Roundcube also offers many of the functions you can find on iRedMail including message searching, folder manipulation, multiple sender identities, support for the external SMTP server, import/export, and unlimited messages and users.
RoundCube features LDAP connection, address book management, IDNA and SMTPUTF8 support, share/ global IMAP folders, import/ export options, threaded message listing and more.
I really like Horde's mobile UI, and the mail client was pretty easy to install separate from the rest of it. SquirrelMail and RoundCube are challenging to use on a mobile device. RoundCube has a supposed mobile plugin but I could not get it to work.

Horde is an open-source groupware solution for teams and communities. It offers a webmail edition, a responsive interface and customizable dashboard.
The Horde platform offers a PHP framework with applications and libraries for creating a customized environment that suits your workflow. Your Horde webmail supports POP3 and IMAP protocols and HTML message composition.

Horde is more just a mail client, it is an enterprise-focused groupware. Horde is capable to read, send and organize mail correspondence, fully manage contacts, calendars, tasks and various notes. Horde is using its own PHP framework with libraries to insure possibility of building custom solutions.
More than just a mail client, Horde is full-fledged enterprise-ready groupware. The Horde suite is browser based, and includes web apps for reading, sending and organizing email, managing and sharing calendars, contacts, tasks, and notes. In addition, the Horde project provides a PHP framework with libraries and apps for building out a customized working environment.

Horde is a fully open source webmail client and “enterprise-ready, browser-based communication suite.” Although its functionality isn’t quite as advanced as that of Office 365 or G Suite, it does offer more productivity features than the traditional webmail client, as well as advanced access controls for more granular user permissions.
Not sure which to choose? According to the official cPanel documentation here's the difference: Horde is for users who need a full suite of features that includes mobile email access and advanced productivity tools. RoundCube is for users who need a user-friendly web interface with some additional features available.
As of 4 April 2023, the Horde webmail client will no longer be available on servers. Before then, you will need to switch to either App Suite or Roundcube. When Horde is shut down, calendar events and contacts will automatically be migrated to Roundcube. The shutdown of Horde will not affect your email.
The Horde Webmail client has been deprecated since it is no longer being developed. This signifies that the developers are no longer providing upgrades to suit future requirements.
Horde is not compatible with CCS. Horde uses its own calendar and contact service. Please note that Horde reached End-of-Life on November 22, 2022, and was removed from cPanel in version 108.

Horde Webmail is a free, enterprise-ready, and browser-based communication suite developed by the Horde project. It is a popular webmail solution for universities and government agencies to exchange sensitive email messages on a daily basis
You can access mails through the web client or via dedicated apps for desktop (Windows or macOS) and mobile devices (iOS or Android). However, only premium users can use the desktop apps.

Verdict
As Horde is discontinued, Roundcube will replace the horde email consumers.