From the Super Mario Wiki
The Super Mario Bros. Super Show!
Prior to the events of the episode, Gramma had fallen ill, prompting Princess Toadstool to pay her a visit, along with Mario, Luigi and Toad. Due to the fact that King Koopa had stolen all the firewood from the local village, Mario, Luigi and Toad stay behind to gather more, while Princess Toadstool ventures on to visit Gramma.
Meanwhile, Gramma's firewood runs low, when King Koopa, dressed as a messenger, tricks her into thinking that she had won a year's supply of wood, and convinces her to go into town to claim it, so that he can dress up as her and trick Princess Toadstool once she arrives. King Koopa's plan nearly works, although Princess Toadstool escapes from the cottage while Pine explains to Gramma that everyone's firewood had been stolen. Mario, Luigi and Toad tell Gramma to stay behind while they go off to rescue Princess Toadstool, but their absence allows for three Koopa Troopas to kidnap her.
After King Koopa kidnaps Princess Toadstool, he and his Koopa Troopas bring her and Gramma to his lair in a nearby cave, where he has been hoarding everyone's firewood. However, Mario, Luigi and Toad wear the Big Bad Wolf's spare winter coats to scare off King Koopa, as the Big Bad Wolf wants to get back at him for fighting with him earlier on.
With everyone's firewood restored, Pine explains that everyone would be able to keep warm for the rest of the season. Gramma then thanks Princess for visiting, and suggests that maybe next time, she should come and visit her instead. The six laugh in unison, and Princess Toadstool gives her grandmother a kiss on the cheek.