To export Webmail emails to your computer's hard drive, the best solution is eSoftTools Webmail Backup Software. This software allows you to easily export Webmail emails to your hard drive and other locations like Roundcube, Horde Mail, and more. You can save Webmail emails in various formats such as MSG, HTML, EML, PDF, and more. The software also offers a free demo option, enabling you to back up 20 emails from each Webmail folder without any cost.