Q: Can 2015 IMac use earlier system from external HD ?

Please forgive me for this question.  I know I'm still a computer dunce and always will be.

But my IMac 2010 using OS 10.6.8 is freezing but the cursor still moves.  After a minute or so it comes to life again.  But from what I've seen on the Apple Forums the problem means it's time for a new one.  I know 10.6.8 can't be installed on a new model.  Lotsa $$$ and important files are on there, backed up constantly on Time Machine.

My IMac HD with 10.6.8 is backed up in its entirety on an external HD.  If I do have to buy a new 2015 IMac, will I be able to open the old programs and files from the external HD running the 10.6.8 OS instead of the new later system that will be on the new IMac?

Thanks so much.

Gina