Vertically - This is your application, APIs, .Net, operating system etc. that may define requirements on Oracle Client version, and vice versa.
Horisontally - "on the wire" or connectivity wise - Oracle certifies client - server interoperability at least two releases or major versions back/apart, so yes, 10.2 is/was* supported. See MOS interoperability matrix for your specific case.
(*was since 10.2 Database is out of support or even Extended support by now. Perhaps it is time to upgrade the server side also ;-))