Having the tail cocked or tilted up: as, the cocktailed flycatcher, Alectrurus tricolor.
Said of a horse having the tail docked so that it points obliquely upward like the tail of a cock.
The Century Dictionary (Public Domain)
Use "cock-tailed" in a sentence
"Because these animals tended not to be thoroughbreds, cock-tailed came to denote horses of mixed pedigree."
"And very often Tom caught them just as they touched the water; and caught the alder-flies, and the caperers, and the cock-tailed duns and spinners, yellow, and brown, and claret, and gray, and gave them to his friends the trout."
"* The cock-tailed beetle has earned this name in the West of"