As if depraved Emperor Caligula Hux wouldn't be 10000% into watching the entire court illicitly ride his steed. He'd probably put on a fake stable master costume (a fake moustache, nothing else) and literally pimp his ride. Then he'd throw off his disguise, "catch" them in the act and punish them mercilessly, sexily, insanely.

"Step right up, step right up, come slake your treasonous lusts upon the Imperial steed! The Emperor will never know!"

*winks, moustache falls off*

"Safe, fun, anonymous! Discretion guaranteed!"

*hot pokers and recording equipment falls out of the bag he's poorly hiding behind his back*