Oh dear - yep Cooper's are very adept at arboreal hunting. Have seen then take a Mourning Dove.Untrue here. Here they sing all winter long.
They have been deathly quiet (essentially absent) since a hawk killed my pullet Sylvie. At least 1 Cooper's Hawk is hunting the birds (including chickens) in my yard.
They r my fear here too, I want to put a covered run up in the Spring. One of those hoop coop contraption I am researching netting. I have heavy snow load here though...