How to add PHP code snippet to all Post pages?

I recommend you use hooks to insert your code from functions.php instead of modifying a theme file. Otherwise you have to make the same change to the template every time you update the theme.

http://codex.wordpress.org/Plugin_API/Action_Reference

Many themes offers its own hooks so that you don’t have to code as much. For example, Genesis framework documentation lists available hooks you can use to insert any PHP in various places.

Genesis Framework: http://my.studiopress.com/docs/hook-reference/

For example, you can use genesis_before_loop hook to add your php code just before the loop of single post. Try reading your theme documentation to see if any hooks are available out of package. Otherwise, you will have to read the official documentation to figure out yourself.