[... Water Tribe games. Aside from playing around in the snow and ice, most games involve a lot of physical exertion or involve showing a resistance to pain. Seeing as there's no snow and Sokka really isn't keen on being utterly curbstomped at stuff from his own culture...]

... yeah, I don't really think there's any Water Tribe games that really apply. Because... no snow. [A convenient enough reason.] What about Earth Kingdom stuff?