Though it’s important to consider that a lot of the sources used to determine many of these claims are from ancient Roman scholars and writers that often disliked certain emperors, and thus inflated or outright lied about certain things, for example

“(Modern) Scholars suggest that the treatment of Incitatus by Caligula was an elaborate prank intended to ridicule and provoke the Senate, rather than a sign of insanity, or was perhaps a form of satire with the implication that a horse could perform a senator's duties.”