That’s what I’m talking about. AoE3 devs created the name of the unit basing on an element of their clothing. Overall, there is nothing special about it, as there are more similar cases in the game, albeit based rather more on armament rather than clothing (like Yumi Archer, Qiang Pikeman, Changdao Swordsmen etc). But when basing on weapons, such a term-formation by devs makes at least some sense (as it allows to distinguish a such unit from other units of this type), whereas in the case of Czapka Uhlans it does not.
It would be different if that name would base on some famous unit or regiment called this way. But as I said before there were no units called Czapka Uhlans in Polish or Austrian, Prussian, Russian etc armies (if you know any, please share with us) and It just looks like the devs creation.
Highly debatable thesis.
I agree, there would be some better cavalry units for the Polish UU, even apart from the Winged Hussars (which are must-be for this faction).
Stats do not matter as long as these can be just changed. So that is not an argument. However, as you have noticed, the Magyar Hussars are also not suitable for other reasons.
This is a good, though difficult question. I hoped to hear some interesting suggestions.
For me, the best option for a unique cavalry unit of the generic faction of “Germans” in AoE3 timeline, would be a unit called just “Reiter”, as it is a generic german word for rider/cavalryman/trooper/equestrian.
One of these - Black Riders (Schwarze Reiter) are already in the game as mercenary unit (and de facto Swedish UU btw). Schwarze Reiter were basically a kind of poor cuirassiers, but in the West the name “Reiter” has also spread as a general term for all other German-style cavalry (understood as various types of pistoliers):
Reiter
So, they could be added as melee cavalry with similar role as the current AoE3 Uhlan (high attack, low HP), but with additional ranged attack like Swedish Hakkapelit. Unfortunately, there is already one unit in the game with a homologous name - Dutch Ruyter (or Ruiter - again rider/horseman/etc).
Another solution would be to remake the “Germans” faction and narrow it down to the Austrian Empire only. Then units like the Croat Riders, known mainly from Habsburg Armies would be justified in some way as UU for “Austrians”, but it seems to me that we would go a bit too far here and that would implicate more changes, so this variant is a topic for a different discussion and thread.