A hink pink is a word play riddle where the answer consists of two words that rhyme and fit the given clue. In this case, the hink pink "keeps a cat's paws warm" could be "toasty toesies." The answer plays on the idea of keeping a cat's paws warm with something cozy and rhyming with the clue.
kitten mitten
sweet feet
Cats paws can be pink or gray.
The hink-pink for "The extra cash that Santa keeps in his shoe is his" is "Yule mule." In a hink-pink, the goal is to create a pair of rhyming words or phrases that answer a riddle or description. In this case, "Yule" rhymes with "shoe" and "mule" rhymes with "cash," making it a fitting hink-pink for the given statement.
boot loot
because they are about to die
cash stash, boot loot
Thin inn is the hink pink for skinny hotel.
The hink pink for "boy's test" is "lad's quiz."
lathering gathering is the hink pink for a group of men shaving
"Man pan" is a hink pink for male pot or masculine skillet.
Dark ark is a Hink-Pink for Noah's boat with the lights off.