defamation. You're defamed when someone makes an untrue statement that injures your reputation ... and we're not sure that a face full of frosting ruins a politician's reputation. Politics is a contact sport and free speech reigns supreme. It's also probably not an invasion of privacy unless perhaps the photographer was trespassing at the cake-throwing event.
Copyright. If the photograph was reproduced without authorization, the opponent may have committed copyright infringement. The copyright owner -- probably the photographer -- could bring that claim (not your friend). Copyright lawsuits in political campaigns are used strategically, or to distance a copyright owner from a candidate. Some political infringements are excused as a fair use and most are resolved long after the campaign has ended.