It's possible with
$('#iframe_id').contents().find('.stuff_to_modify).addClass('whatever');
But it's also possible using window.postMessage events, by sending a do_something message to a script from the iframe, which does the modifications when the message is received (adds that class).
I was wondering which is the way I should go, and what are the differences between these two methods (drawbacks, advantages).
The jQuery method seems nicer because I don't need to include any script in my iframe anymore