Cicadas
Other maybe than birdsongs in spring, I can't think of an animal sound more tied to a particular season than cicadas in summer. In Ohio as kids, we called them locusts and marveled at the nearly intact dried skins they shed during molting and left clinging to trees, often willows or walnuts .

In Latin, cicada means “buzzer” and they buzz by vibrating membranes on their abdomens, which are mostly hollow and work as amplifiers. They modulate the buzz by angling it off the tree they’re perched on. Each species has its own song.
(image via the New York Public Library Digital Gallery)