I have a DTSX file in a project I\'m taking over. I have Visual Studio 2005 Pro, but it just opens it as an XML file. SQL Server Management Studio 2005 does the same.
Additional answer for Visual Studio 2012:
You can open .dtsx along with their corresponding .dtproj project files with the SQL Server Data Tools Business Intelligence (SSDT-BI) add-in:
http://blogs.msdn.com/b/mattm/archive/2013/03/07/sql-server-data-tools-business-intelligence-for-visual-studio-2012-released-online.aspx
http://www.microsoft.com/download/details.aspx?id=36843
If the projects were created with an earlier version they will require an upgrade.
I did have some hang ups installing this - the install would spin on "Install_VSTA2012_CPU32_Action" and similar steps. It wasn't until I did a repair inside of the same installer did it install completely.