Many versions of the "Cinderella" story inflict Body Horror on the cruel sisters/stepsisters. They hack off parts of their feet trying to get the glass slipper to fit. In the Grimms' version, their eyes are pecked out by birds. In some Spanish-American tellings, they grow horns and donkey ears. In one version the selfish sister has snakes come out of her mouth whenever she tries to speak.
In one of Grimm's fairy tales there's a story about a man who gets turned into a black, fire-breathing poodle.
Since he was the bad guy of the story, after he's turned back they have him drawn and quartered. Yeah, that's better.
The Grimms have quite a bit of Body Horror in their stories. Their version of "Little Red Riding Hood" had the woodsman cut the wolf open so that the grandmother could escape, then pack the Wolf's stomach full of rocks and sew it back together — afterwards they kick him in the river when he wants to drink, so he sinks to the bottom to drown. You could say he deserved it, but still, to tell this to children...
Also from the Grimms is "Snow White", though to a lesser degree. The evil stepmother crashes the wedding of Snow White and the prince. Unfortunately for her, everyone there knows all about her murder attempts on Snow White. Therefore, the stepmother is forced to dance in red-hot shoes. As if feet that are burning aren't bad enough, she has to dance until she dies from exhaustion.
The abomination called the Nuckelavee from Scottish folklore. It can only be described as some sort of rider-fused-with-horse centaur with no skin that breathes disease. So even if you escape it, you've got the more common sort of Body Horror to contend with.
The Curupira has feet that are turned to face backwards, flaming hair, and green teeth.
There are many variations of a fairy tale, where a man hacks the paw or tail off of an animal (a cat, a rabbit, a wolf, a snake, etc), only to find that the animal was his wife, who regularly would turn into that animal. He would find this out by coming home and finding she was missing the limb he hacked off. And this is treated like an embarrassing incident by the wife. One variant has a woman turn into a snake and her nephew hacks the tip of her tail off. This translates to the entire one half of her foot being chopped off, and she insists that she just stubbed her toe in the middle of the night. Eek!
Many Fairy Tale stories actually involve characters having their heads cut off or their bodies torn apart, and somehow they come back to life after their bits and pieces are sewn back together. Ew.
Some of the tales manage to soften it by specifying that a magic liquid is used to seamlessly put the pieces together and basically make the body as if it died of natural causes, before bringing it back to life. Still, the idea of a person being casually torn into small pieces (which is how most of those sorts of tales go) is plenty body horror.