Discover the original OS of a datafile from a oracle backup
Mount the database and make a level 3 datafile header dump:

alter session set tracefile_identifier = 'header_dump';
alter session set events 'immediate trace name file_hdrs level 3';


In the trace file, you will find this section:

Platform Information:    Creation Platform ID: 13
Current Platform ID: 13 Last Platform ID: 13


The platform ID identifies the platform of the datafile, and that is all what matters.
You can match the platform ID to platform name by using the information in the V$TRANSPORTABLE_PLATFORM view. For example platform 13 is x86 Linux 64-bit:

SQL&gt; select platform_name from v$transportable_platform where platform_id = 13;

PLATFORM_NAME
-------------------------------------------------------------------------------- 
Linux x86 64-bit