alt Hacker NewsIf you are uploading it to a website you are sharing it. Even if the image is supposedly "private" you have to assume it will be leaked at some point. Remember, the cloud is just someone else's computer, and they can do what they want with their computer. They may also not be entirely competent at their job.
Yes, once something has been shared (or stolen), you lost control over it, be it information or an image. EXIF data is fine, if it never leaves your device or if your device is not compromised.