When Princess Toadstool traveled to the Mushroom Woods to visit her sick grandmother, Mario, Luigi and Toad had to stay behind in the village to gather firewood, leaving Princess Toadstool alone and defenseless. As Princess Toadstool continued onwards through the woods to reach Gramma's house, the Big Bad Wolf spotted her, and remarked to himself that if could beat her to Gramma's house, he could quickly ambush and eat her.
The Big Bad Wolf eventually arrived at and snuck into the cottage, but was beaten to the punch by King Koopa, who had already lured Gramma away, and was dressed up as her. The Big Bad Wolf and King Koopa got into an argument, but King Koopa ordered his Koopa Troopas to tie up the Big Bad Wolf and get rid of him.
Later on, the Big Bad Wolf loaned his spare winter coats to Mario, Luigi and Toad, which they wore to scare off King Koopa, who had eventually captured Princess Toadstool and Gramma. Grateful for their rescue, Princess Toadstool told the Big Bad Wolf that he wasn't such a Big Bad Wolf after all. The Big Bad Wolf assured her that while his is big and bad, he just didn't want King Koopa cutting in on his territory. Before leaving, the Big Bad Wolf told Princess Toadstool to ditch the red hood she had been wearing, as it wasn't a safe thing to wear in the woods. He was never seen again after this episode.
This is clearly based off of "Little Red Riding Hood".