Ashley Reese at Jezebel posits that hating women is actually part of Trump's brand.
Trump’s disdain toward women is well documented; it’s a meticulous catalog organized by target, temperament, and scales of fuckability. It’s his bread and butter. It’s his joie de vivre. It’s giving far too many men exactly what they want to hear. It’s safe to say that most Americans will go about their day blissfully unaware that Trump mocked Daniels’s appearance. But elsewhere, the attentive members of his base will revel in the degradation.
The Trump brand lives on retrograde sexism, whether it’s calling women ugly (Daniels), fat (multiple examples), portraying them as bumbling ditzes (Christine Blasey Ford), or vengeful liars (any woman who has accused him or his friends of sexual misconduct).
Trump's "horseface" tweet was not a careless mistake either. According to Talking Points Memo, Trump not only thought about the tweet, but workshopped it with those around him. Per The Daily Beast:
Well before Trump mocked Daniels’ physical appearance, he trial-ballooned the “horseface” dig privately—among White House aides, close friends, and acquaintances. One source close to Trump even recalled him saying in passing, “that fucking horseface.”
The president often tosses around ideas for snide new nicknames in smack-talk sessions with associates, if only to gauge their reactions. And, as in past cases, the “horseface” incident saw Trump defying presidential norms (whatever those are anymore) and ignoring senior aides and confidants who advised him simply to let the matter go.