Nope. Can't be a picture hanger. Gravity is the other way round (the acorn would be upside down).
I'm still inclined to go with the top-hinged cabinet door. The design of it means that the bottom of the door has to sail past the shelf behind. It may belong to one of the interior compartments of a writing bureau.
To estimate the thickness of the wood that it belongs to, measure across the outside of the "U" - it must be inlaid. If it's 1/2", then it's probably off a cabinet door. If it's 1/4" or 3/8", then it's more likely to be from an interior compartment.
edited to add:
Also think in terms of stationery boxes and humidors - small boxes that don't move much and don't need a locking lid.
I have just realised what a prattish and ridiculous suggestion I made on my post of Sep 17th! I've just noticed the 22mm X 22mm measurement!
Bloody small horse! Sorry! It looks like a bit of a 'sweetheart brooch' mackled up to something else, no idea!
I may well be way off base here, but might I suggest some sort of Canadian connection?
The Thistle (symbol of Scotland) seems to take the form of a stylized Maple Leaf (long the symbol of Canada, well before 1965 when we changed our flag). Much of Canada was settled by Scottish pioneers, hence, this could explain why this item seems to have the stylized outline of a Maple Leaf.
If this is the case, it could perhaps be a lady's brooch of the type from which a lady's watch would have been suspended, circa 1930's. Also, it could be some piece of ceremonial or mess dress accoutrement. For example, it could perhaps form part of the fastening device for a pistol holster (just a guess) for patrol dress - or possibly a fastening device for a sporran?
Anyway, the possible Canadian connection is just a thought. Certainly, I've no proof.