I think it's a hidden "green agenda" message from Hollywierd.
When he rides real fast, the dead bird's wings spread out, generating a lift (like an airplane wing). Then Tonto clamps his legs tight against his horse. This slightly lifts both Tonto and the horse, causing less weight, and thus, less down-force on the terrain, resulting in less damage to the environment.
It also gives Tonto more "miles to the Gallup".
I totally see that logic..lol. No carbon “footprint” to track. BRILLIANT!