The UK’s culture minister, Ed Vaizey, has warned that taking a screenshot of a Snapchat message and sharing it without the consent of the sender is illegal in the UK. When asked about the legality of Snapchat, he said, “Under UK copyright law, it would be unlawful for a Snapchat user to copy an image and make it available to the public without the consent of the image owner. The image owner would be able to sue anyone who does this for copyright infringement.”
If this is the law, then it doesn’t only apply to SnapChat, but also to photos that people send via iMessages, MMS, or any other non-public messaging service. I would assume this wouldn’t apply to photos attached to tweets, unless a user’s account is private; there is an understanding that tweets are public. And what about Facebook? You choose whether your page is publicly accessible or not; if it isn’t, then the law should apply as well.