Adding videos directly into the body of an email is not an option (this is the case for any video platform and any email provider).
What you can do is take a screenshot of the video (or a GIF) and use that as an image linked to the actual page where your video is. That way, your image will look like the video and when the reader clicks to play, they'll be taken to the page where your video lives.
This example shows how you can do it on Mailchimp (click below):
The process should be the same or identical to any other email campaign software.