As someone else suggests..
http://dev.mysql.com/downloads/mirror.php?id=382641
..fixes the problem.
I had v6.2.3 installed after I had vs2010 installed and the MySQL driver was not shown in the list of the Database Connect dialog. I wrongly assumed I should use the .NET ODBC drivers instead and it caused all sorts of problems. Although I could easily connect to the DB using codebehind, the server explorer wouldn't connect to the DB.
Luckily after uninstalling 6.2.3 and installing 6.3.0 (from the link above) the MySQL driver was added to VS2010, and I was able to connect to the database and see it in my server explorer.