Fortunately English is also rife with horse-derived idioms. And yes, hack in the derogatory sense (e.g. "talentless hack writer") is derived from hackney ("ordinary horse used for menial work"), itself derived from the borough Hackney in London where many such horses used to be raised.
...oooh!Hmm, a mouse-musume, is it?This gets my blood pumping as a scientist!W-Who do you think you are!?
You're just some shady hack of a youkai from who knows where!
You're being rude, you know!
Original uses uma no hone (literally "horse bones"), a Japanese idiom referring to a person of uncertain/dubious origin.