Is there an easy way to add an email (from Outlook) into a card on Trello?
The short answer is no - because you used the word Outlook.
Superuser.se has a question How to save a mail into an .eml-file with Outlook? and although it looks like it might be possible I wouldn't classify any of the solutions as easy.
Thunderbird on the other hand lets you save an email as an .eml or .html file via the right mouse popup.
Then you'd simply add the .eml or .html as an attachment to your card in Trello. Then if it needs to be viewed, click on the attachment link on the card. If you used an eml file then your browser will probably download it as normal rather than launch it directly as it would for the html file, but once downloaded, double click the .eml file and your email client will pick it up and display it. Again - for me this is Thunderbird and it works beautifully.
Outlook, however - mmmnot so easy.
Two workarounds come to mind though:
You can add email from Outlook or any other mail client (desktop or mobile) via Emello. You can assign custom dedicated email addresses to any of your boards and lists. This should fix your work flow issue.