From the Super Mario Wiki
The Mushroom Woods is a forest made up of large, tree-sized Mushrooms, located towards the far end of the Mushroom Kingdom. In the center of the woods is a village populated by Mushroom People, one of whom is a woodcutter named Pine. Gramma Toadstool lives in a cottage that lies across a river on the far side of the village. The Big Bad Wolf also dwells within the Mushroom Woods, giving the place a somewhat dangerous reputation. The Mushroom Woods was only ever seen in The Super Mario Bros. Super Show! episode "Little Red Riding Princess".
The Stolen Firewood
King Koopa traveled to the Mushroom Woods during the winter season at some point, and plundered all of the villagers' firewood. Whether King Koopa did this as part of a threat or just simply to agonize the citizens is unclear. With no more firewood to warm their homes, the cold winter air soon caused everyone to freeze up, to the point where they were encased in ice.
A short while later, Princess Toadstool passed through the Mushroom Woods with Mario, Luigi and Toad, on a journey to visit Princess Toadstool's sick grandmother. Upon their arrival at the village, they discovered that Pine and his family were frozen. After a brief encounter with King Koopa, Toad thawed everyone out, and Pine was able to tell them of what King Koopa had done.
Journey to Gramma's
Princess Toadstool was unable to wait any longer, and asked her friends to gather more firewood to thaw out the rest of the villagers, while she continued through the Mushroom Woods to reach Gramma's. Princess Toadstool was unaware of the fact that not only was the Big Bad Wolf spying on her, but King Koopa was as well. However, the two villains were unaware of each other's presence, and both intended to ambush Princess Toadstool at Gramma's house.
King Koopa reached Gramma's house first, and duped Gramma into leaving her cottage by convincing her that she won a year's supply of wood which she had to claim by going into town. While King Koopa waited for Princess Toadstool to arrive, the Big Bad Wolf snuck into the cottage, only for three Koopa Troopas to kick him out. Princess Toadstool soon arrived at the cottage, and at first was fooled by King Koopa, who had dressed up as Gramma to trick her.
Duping King Koopa
While King Koopa attempted to catch Princess Toadstool, Gramma arrived at the village, where she learned that King Koopa had tricked her. Mario, Luigi and Toad announced that they would go back to the cottage, while Princess Toadstool managed to escape from King Koopa. Mario's group eventually surrounded King Koopa in the middle of the Mushroom Woods, but he was saved by three Koopa Troopas, who had captured Gramma. Grabbing Princess Toadstool, King Koopa rode off with the Koopa Troopas on one of their snowmobiles.
Mario, Luigi and Toad followed the snowmobile tracks into a cave, which led them to lair where King Koopa had stashed all the stolen firewood, and was keeping Princess Toadstool and Gramma prisoner. Dressed up as wolves, Mario, Luigi and Toad scared King Koopa out of the cave, and revealed that they had used the Big Bad Wolf's spare winter coats to do so with, mainly because the Big Bad Wolf wanted to get even with King Koopa.
Afterwards, the stolen firewood was returned to the village, and the Mushroom People were able to keep warm up through to the end of winter and Gramma Toadstool enjoyed seeing her granddaughter again after Mario and his friends saved her.