You can open the DTSX file in Notepad to determine what version of SQL Server it was created with and look at the "PackageFormatVersion" value. The exact line should look something like:

<DTS:Property DTS:Name="PackageFormatVersion">n</DTS:Property>

The "n" will be a number of one of the following, and I can't find anything concreate from Microsoft on this it just trial and error (and a bit of Googling):

2 = SQL Server 2005

3 = SQL Server 2008 R2 (probably SQL Server 2008 as well)

6 = SQL Server 2012

? = SQL Server 2014 (if someone has those tools loaded I am not sure what value it will be for this version).

Since the XML structure changed a good bit with SQL Server 2012 you are likely not going to be able to easily open it or modify it to open without errors.

If you have the whole project the DTSX file was created with you when you open that project in 2012 it will upgrade the package for you. This would be the best route if you cannot get your hands on the BIDS install for 2008 or 2005.