If we're talking about the cavalry units, I want to say that I think the heavy chariot needs a slight adjustment: currently, the heavy chariot gains +1 movement if it starts its turn on flat, open terrain. I think this should be changed to "has +1 movement while on flat, open terrain". Civ 6 calculates movement cost by the tile you're entering, not the one you're currently in. If my chariot is currently in a hill tile, sure, it would be at a disadvantage, but if I move down onto a plain, I could really speed up. Moving from a forest tile into another forest tile is not penalized any differently than from an open tile into a forest tile, therefore chariots shouldn't be penalized for where they start.
In practice this could mean you could start in a hill, move onto flat terrain (which would cost 1 movement, leaving you with 2) and then re-enter a forest or hill.
Also, I like
@Boris Gudenuf 's idea with Cuirassiers. What about light cavalry though? Classical -> Industrial is a long gap. My understanding is that through most of the middle ages in Europe, cavalry were primarily heavily armored due to a number of factors. Lancers are a lightly armored melee mounted unit, but since they would come around ~the Renaissance, I think that might be too soon. What about
this wikipedia article on light cavalry raiding? It seems to have taken place during the medieval period (mid 14th century).
Another article seems to indicate the raiding was done by knights or men at arms of some kind, "or swift mounted raids called
chevauchées, with the warriors lightly armed on swift horses and their heavy war horses safely in the stable".
To me, this sounds like a knight that isn't wearing heavy armor, on a lighter, faster horse using raiding tactics. If these riders were caught, they would not have the defences they normally would. They'd have lower combat strength and defense but be faster. Sort of puts a stick in the spokes of having a medieval light cavalry unit, unless someone else knows more about this than I do.
On the topic of raiding with light cavalry though, if such a unit could exist, it would be interesting to see something like "pillaging an improvement grants +0.5 movement, pillaging a district costs -1.5 movement". Obviously horsemen and cavalry don't have this ability, it would have to be just for that unit. Would make them a lot stronger for pillaging enemy tiles, which seems to be what they were designed to do in real life, but not good at pillaging districts (because I think that would make them too strong).