This article lists some alternatives to DreamHost's Webmail service.
Hosting with non-DreamHost mail
New! DreamHost now offers Google G Suite.
G Suite is a collection of apps to help organize and simplify your organization's workflow, and includes a mail service (Gmail). For more information about using G Suite at DreamHost, see the following article:
Using Gmail as a Webmail client
Installing your own Webmail client
It is possible to set up any web-based IMAP mail client as a replacement for the default Webmail interface. You can disable DreamHost's Webmail for a domain using the Webmail page. This will free up the Webmail subdomain for you to use with your own Webmail client.
You can install your own version of alternative applications such as SquirrelMail or Roundcube. There are other popular Webmail clients including Horde and Open Webmail.