On horses yes- it's a must- shoulders, hips, and heals all in line with your back not too arched and not too bowed.

When I'm off a horse, my posture is terrible which only makes my back problems flair up even more since I have no curve to my neck or spine. I am constantly hunched or slouched in the chairs at school. I rarely sit properly, unless their is a guest speaker or something and we have to look nice as a class.