If you have migrated your hosting services away from DreamHost, it is still possible to log into your old email addresses. However, it's not guaranteed how long their data will be available for, so it's recommended to retrieve any email as soon as possible to avoid deletion.
How to log into your old DreamHost email
Logging into your old DreamHost email is the same as it was before you migrated away from DreamHost. You would use an email client (Thunderbird, Outlook, MacMail) to connect, but you use DreamHost mail servernames when connecting. That's it. View the following article for instructions on how to log in using an email client.