I have not tried willow but others have and I believe some of the Western Tribes and maybe Northern Tribes used willow for arrows. If goldenrod, horse weed and dog fennel work for arrows, why wouldn't willow.
With any shoot arrows, I believe that you have to use second year growth or older. First years growth is usually light in physical and spine weight in most shoots I have tried. To determine 2nd year growth , look for small twigs growing along the shoot as opposed to just leaves. On first year shoots leaves appear. In the fall, these leaves fall off and next spring small twigs come out where the leaf scars are along the stem. Plus, by the second year a shoot has 2 growth rings to oppose each other instead of just one ring. Pat