You can do it in all versions of TOS (well at least from 1.02 up).
Highlight any program and select 'Install Application' from the 'Options' menu. From there you can associate a file extension with that program. From that point on, you can double click an associated data file to load it automatically into the application.
In order for these file associations to survive a reboot, you must save the desktop.
Mega"SST" 12, MegaSTE, STE: Desktopper case, IDE interface, UltraSatan (8GB + 512Mb) + HXC floppy emulator. Plus some STE's/STFM's