Personal experience in observing homosexual behavior in horses, both stallions and mares, who all try to flirt and mount the same sex. Mares will sometimes mount other mares when they're in heat, because the roiling pool of hormones that horses have drive them fucking crazy, hornier than a five-headed unicorn. A few mares that I've seen get with other mares also exhibit antipathy towards stallions, even during times of rut, so horses having a preferred sex for banging is totally a thing; the idea that it's for dominance, as it is for dogs and a few other animals, is bullshit. Horses compete for dominance by biting and kicking the fuck out of each other, and that's for things like who gets dibs on food or at the watering hole, not mates.
It goes the other way too. A friend of mine (who was lucky enough to have the lesbian mares of which I spoke) had a stallion who only went for geldings or other stallions, was aversive to mares (not violently so, he just avoided them), and even had a whinny that honestly made him sound kinda... fruity, I think is the best descriptor.