Can a university try to punish a student for things they say or do on Snapchat? Yes. Is the university within its rights to do so? Possibly not. It of course depends on what's posted or said on Snapchat. The student does have an obligation to live by the school's policies, the code of conduct, for example, or other policies that may be at play. The student does also have certain rights, freedom of speech, although it may be a limited, right? They do have certain rights to express themselves.
It depends on what's posted. Is it sexual in nature, racial, threatening? That would be a certain consideration. Is it something that's supposed to just stay that somebody just simply disagrees with or is maybe not a popular opinion or message and the school is trying to take action against the student? In that regard, that's not an unusual situation. Schools can be unreasonable and overzealous, regrettably. Having an experienced attorney advisor will be your best ally in understanding and protecting your rights and interests. It can help you best understand and navigate the process moving forward.