I honestly don’t know if it has a core in it, but it’s not soft or floppy. It has a tiny bit of give, but it’s mostly stiff and has a bite to it.
I ride in open spaces, too (not enough room for hay fields AND an arena), and I’ve never been worried about having enough stop with this noseband. Several years ago I read a blog by someone who had attended a cross country clinic with a BNR. The writer’s thoroughbred was misbehaving and the BNR had her remove her bit and use a spare hackamore noseband that he kept on hand, and she had a much better ride. I wish I could remember which blog it was. I’ve also heard others talk about foxhunting in them. At the end of the day, though, the only thing that matters is what you feel secure using and what your horse listens to best.