Did you know horses aren’t strong enough to support your weight at a standstill?
Horses don’t engage their core at a standstill, they also don’t engage their longissimus (the muscle you sit on).
Because of the way their biomechanics work, they have to be in motion to engage their longissimus (back) and abdominal muscles to support your weight. If you think of it like a pulley system, when they lift their hind leg to pull it forward, the movement of their hind end -tibia, femur, pelvis, etc- will engage their muscles, ie biceps femoris, TFL, glutes, semitens, etc- these muscles have attachments along their spine, sacrum, ilium & thoracolumbar fascia, which your Longissimus and abdominals attach to. It’s also where your Latissimus dorsi attaches to, which pulls your front limb caudally. Your longissimus also shares attachment points with your traps, which also aid in movement of the front end. Therefore, when those muscles are engaged from the horse moving, your Longissimus and core muscles will engage.
Now let’s connect that to something like their digestive system- take a look at the picture of the different innervations coming from each vertebrae. That’s what you’re sitting on without muscle engagement to help ease the compression from your weight.
All that said, we also have to consider the importance of correct riding as horses will try to cheat to avoid engaging these muscles while being ridden. Just like us, in the moment, it’s easier to workout without keeping your core engaged, but how’s your back feel after a workout where you didn’t engage your core vs one where you did?
You have to ride correctly to help them engage these muscles. Get them off the forehand and make them move their hind end.
Still don’t believe me? Try it. Get down on all fours and have someone sit on your back. Now stay there for the same length of time you’d make your horse stand (whether your standing at a rodeo between rides, sitting around after a lesson, etc), then tell me how your back feels.