There is no provision in Mail (or email in general) to automatically include a profile picture in the email. Other than automatic signatures, that is. Mail on the iPad can't send pictures in signatures. Not with a lot of workarounds that you'd know you did. So:
It's more likely that your friend has their FaceBook account linked to contacts on their device, which would put your FaceBook profile picture in their contacts, and then display it whenever they receive an email from you.
When you see an picture in Mail on your end, it's because the picture is associated with that email in your contacts. If you have Contacts enabled in your FaceBook settings on the iPad, then it will import your friend's FaceBook profile pictures along with their contacts.
Which is the reverse of what I think is happening on your friends end.