If you have tight hamstrings or glutes, other areas might help compensate to get you through a squat, but there is nothing to help your hips, adductors, or hamstrings when you’re awkwardly straddled over a horse’s back. Sit in that position long enough and your flexibility will improve.
Better flexibility means better range of motion, which equates to improved, heavier lifts. Your calves will also get a good stretch when you ride in the correct position: feet in line with the knee, heels down, back straight. Improved flexibility and reduced tension will lessen the chance of injury when you play a sport or lift.
More than anything, riding can help improve weaknesses. Whether the problem is coordination or flexibility, you’ll see progression and reap major benefits in sports, hobbies, and daily life. So saddle up!