[c3o]

There is no such thing as "fair use" (or the "three-step-test" which you refer to) in EU copyright law. There is a defined list of exceptions (almost all of which are optional for member states to implement), and "link snippets" are not one of them. Every act of copying/making available not covered under those is forbidden.

Plus, as another commenter said, this is not a copyright, but a related right – certain aspects of copyright like the requirement for the work to reflect some amount of original human creativity to enjoy protection do not apply.

You claim most links do not include snippets, but given the popularity of Facebook, Twitter & Co for sharing links, I'm not sure that's still true. Even then: Even the title of a page alone is a snippet (not specifically excluded from this planned regulation), and I bet the majority of hyperlinks on the web do include the title of the linked-to page.

As for the argument that only FB or Google would argue that small publishers will be disadvantaged by this, I refer to this lobbying organisation by independent publishers: http://mediapublishers.eu