One hink pink for Santa's cut facial hair would be Santa's sheared beard.
boot loot
shelf elf
spare hair
fair hair
shag wag
big wig
hair care
care bear
pig's wig
The Hink Pink for a holiday donkey is a Yule mule.
Thin inn is the hink pink for skinny hotel.
Fake bake is a Hink-Pink for counterfeit cook.