I'm not an expert but I do have experience with sport and mock melee combat (albeit on foot) and I think the discussion about polearms from horseback being unwieldy is mixing up a lot of different issues. Especially when someone says something silly like you're going to hack your horse's head off (it's like imagining people hack their own limbs off by using swords improperly, which never really happens). First, using anything from horseback is lot more difficult than using it on foot, second, how difficult the polearm would be to use has more to do with how top-heavy it is as much if not more than how long, and third, how ambidextrous a user would be would affect viability a lot.
The first point should be obvious, but using a polearm from horseback wouldn't be much different than using a longbow like a yumi from horseback, you'd have to steer mostly with your knees/legs in order to use both hands to wield the weapon. In fact, horse archery is a hell of a lot harder than wielding a blade on the end of a pole from a horse, but no questions the validity of that. Horse archers are more common though, despite it being harder, because it's very difficult to counter a horse archer you can't catch. Since melee cavalry is often about shock impact, it's not really much of a big deal what kind of weapon you use (barring lances), so you might as well go with your normal spear or sword instead of something weirder, but there's no real reason you couldn't pick something weird, especially if you were skilled in its use.
In regards to the second point, the unwieldiness of any type of weapon is related to how long it takes to pull back from an attack. Axes, maces, hammers, and especially axes and hammers at the end of poles all have this issue, but you sacrifice attack speed in order to get enough impact from the blow to crush through armor. Of course, a longer weapon that's top heavy is even more unwieldy than a shorter one, and thus using something like a lochaber axe from horseback would be nutters I'd say, but a naginata isn't that top/front-heavy at all really. From what I've seen of people using it, it's actually pretty damn fast, and not just for a polearm either. Granted some of that speed would be lost on a horse from lack of footwork and hip movement, but presumably you'd make it up with the mobility, speed, and shock of the horse.
Lastly, attacking to your off-hand side is pretty awkward on top of a horse no matter what weapon you're using (again, except maybe lances). You also lose a lot of reach doing so, because your arm has to cross your own body. You can twist to a certain extent or stand up in the saddle on the stirrups, but still this is precisely why most cavalry weapons are actually longer, rather than shorter (like horseman using the tachi for instance). However, if you can switch your grip to the left hand side with a polearm without awkwardness, which would be possible as you're not using a shield, hitting the "off-hand" side would actually be more effective. Of course, ambidexterity isn't very common nor easy to learn, so that's probably another reason you don't see it much.
The tl;dr version of this would just be that, we know it *was* used and it probably wasn't more uncommon than wielding an odachi on foot was for a comparison, which is also pretty rare in the records IIRC. So most likely the issue was simply that this required much skill or had specialized use or didn't make a huge difference, but because of the simple fact it was used, and by professional warriors who clearly knew what they were doing and were taking their life into their hands, I don't think armchair theorizing on what was possible or viable on pre-modern battlefields should be stated with the certainty a lot of people do, particularly because essentially no one living has direct experience of this kind of combat (where you are actually trying to kill your opponent or be killed). If someone has direct quotes from something like a Turnbull book on this issue, post them, but I've only encountered contradictory interent speculation on this issue.
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