They have horses in the collectors comic from the New Vegas CE; criticized as a mistake of course.
Inferred lore aside... why would they need horses? Myself, I would like to see wind vehicles and bikes included to the setting.
*Obviously with cheap fusion power, there should be the occasional custom restored electric vehicles found or encountered.
Because horses are literally a game-changer. Without horses, the civilized world as we know it does not progress. Without horses, what arises are the Maya, Aztec, the Olmec, the Inca, the Iriquos, Cucuteni–Trypillia. The horse is one of the prime beasts of burden, beast of transport, and beast of war mankind could ever had hoped for; it has no equal.
The fusion cells will one day end, 'Wind vehicles' are what - sand-skimmers, maybe sail boats; and bikes and other vehicles have increasingly complex designs. It took mankind until the late 1800s to make the Bicycle, for instance.
But a horse? You feed it. You clean it. You get Equestrian girls to whisper in its ear. You can get more horses by giving horses some food and then wait. You can replace them relatively easily, as well, as they're somewhat fragile; and of course, they're dumb as fuck, but that doesn't matter overall. They are self-replicating vehicles. A bit expensive at first, sure, and if you want a strong-ass breed, become a full-time thing for a whole caste of people, but still far more cheap and accessible compared to any mechanical vehicle save, perhaps, the simplest dugouts, for even a cart with its axles and wheels needs a beast or person to move it.
Europe and Asia got to the point where nearly every farm, every man of note, had a horse. We got the electric age with horses on our side (and then killed them off due to the oil-gas car).
Without horses, the world is quite truly fucked; because their course is set. The only hope is that there's enough tech from the overpopulated, over-polluted pre-war world to leapfrog ahead to a higher civilization, but with every passing year, every expanding polity, every looted factory to provide some podunk town with power, that chance diminishes.
Without horses, you have no good chariots, no good workhouses, no barge horses, no mill horses, no mounted infantry, mounted archers, lancers, cataphracts, knights, gendarme, cavaliers, cuirassiers, vaqueros, etc. Their extinction literally cuts out a whole tree of advancement, and old-world civilization will literally never arise again.
