I saw a mushroom house with a chimney right off, so I think Dana could be spot on. Although, my grandma had a couple of similar santa cutters with the sack so full of toys and treats that he was bent over under the weight. It could be a butterfly with the wings out, and that extra bump for the antenna.
I would use it for a peace dove in flight, with a tiny olive branch trailing back from the beak and head. Maybe it's a winged cupid/angel, with the long curve as a drawn bow and arrow? I have to say, it's easy to imagine a large heart with embellishments around it, for Valentine's Day. Maybe a miner/fireman with a headlamp on his helmet?
My daughter is convinced that the lower left is a stereotyped, old-fashioned Native American profile, with feathers on the back of the hair, part of a braid, and the point on the right is a nose. (Like the politically incorrect Redskins sports logo.)Or the profile of a president, with the fringe of hair/wig (Didn't George Washington have a bow on theback of his wig?), and the fancy collar? Maybe I need to go look at some coins...
Knowing how old it is and where it came from could help. It would be awesome if you posted some cookies you made with it, as it's the Rorschach ink blot of cookie cutters lol! It might also be fun to trace it for a template, maybe squished into silghtly different shapes, and send out or post copies to challenge everyone to make something.