I have been working with a haflinger pony who is the world's best pony, goes over anything without breaking rhythm. Naturally. But until I freed up his shoulders, he lacked the ability to rock back and balance himself up. He just dove down, and the jump was awkward.
I didn't stretch him in the way Trissacar mentioned, but doing in-hand lateral movements to free up his tubular little body made his over-all movement and jumping improve by over 50%.
Same idea with the stretching, freeing up those places so that horse can use himself to its full potential.
So I think everyone has good valid points in this thread, Trissacar too.