I made a couple of very fancy cards last year that were intended to double up as decorations to keep and get out each year - one was a star book and one was an accordion style tag book. But they wouldn't be mailable in a regular envelope, so I don't think they'd meet your requirements.
I wonder, though, if you made an ornament something like these -
Snoopy Decorates the Tree by Cook22 - Cards and Paper Crafts at Splitcoaststampers, you could incorporate it into a card as a detachable ornament. Say by stamping some boughs on the card, and hanging the ornament from a brad. I made that some years back before I had a die-cutter. Nowadays I'd have a lot more options available!