I don't know what discipline you do with your horse but this might help:
Here are two shoulder suppling exercises for you to try with your stiff horse.
1. Make a 20-meter box with 4 corners in the walk.
• To give you more control of your dressage horse’s shoulders, do the exercise in counter flexion. (That is, you’ll just barely see his outside eye or nostril.)
• If you’re going to the left, ask for right counter flexion with your right wrist. Stay in counter flexion during the entire exercise.
• At the first corner, bring both hands to the left to swivel your horse’s shoulders around the corner.
• Then, soften the contact without letting the reins get loopy.
• After the corner, walk straight ahead in counter-flexion.
• At the next corner, bring both hands to the left again.
• Do this in all four corners.
• As your horse’s shoulders become more supple, it’ll get easier to spin his
shoulders around the turn without meeting resistance.
• You can tell there’s no resistance when the weight in your hands stays the same as you swivel your horse’s shoulders around the corner.
2. Ride down the long side of the ring, and move your dressage horse’s shoulders slightly to the left and right.
• Walk down the long side of arena.
• Flex your horse at the poll opposite the direction you’ll be moving his shoulders. For example, when riding to the left, ask for a counter flexion to the right by turning your right wrist. Then, take both hands to left to slide your horse’s shoulders over. Move the shoulders over only 1-2 inches.
• Now change to a correct flexion by turning your left wrist.
• Move both arms to the right to pop the shoulders back out to the track.
• Smoothly and fluidly move the shoulders back and forth as you work your way down the long side.
Hope this helps you,