Where are my horses hoves?

[Agema]

A skirmish command would be perfect for light cavalry.

Horse archers are expensive, and I've never seen much use for them in Dom, except those reasonably tooled up for melee as well. I guess they're pretty versatile with a high mapmove, though, if you want to dash armies around quickly.

I do think that hoof attacks for light cavalry is very unrealistic though. Light cavalry were never used as shock troops. Even heavy cavalry are overrated. There's barely a battle in history where there was a decisive cavalry charge against infantry which won the battle.

In the ancient era heavy cavalry were used to drive off light infantry and defeat the opposing cavalry on the wings, not to charge heavy infantry.

In the medieval era, knights were used as shock troops. However, they were successful because the infantry of the era were unprofessional, so tended to be both disorganised and of poor morale, who could be broken up. Whenever knights attacked infantry with resolve and cohesion, the infantry were comfortable winners (e.g. Bannockburn, Battle of the Golden Spurs, lots of battles with the Swiss). The myth of knight superiority is added to by the fact they were essentially the ruling classes, who ensured that their performance and skill was emphasised or exaggerated when historians and poets spoke of their deeds.

[Tuidjy]

You are underestimating charges. Both battles you're mentioning involved really
long spears (pikes) as well as disciplined infantry. And the Swiss were famous
for using them.

Without pikes, standing up to a heavy horse charge would be suicide, no matter
how disciplined the unit. And course, the only thing that pikes are good for,
against horse archers, is impersonating a pin cushion.

Firearms/longbows protected by pikes is what ended cavalry's reign, and mobile,
accurate field cannons eventually beat that combination.

[Agema]

You can have a look at Byzantine tactics. The Cataphract was their battlefield equivalent of a knight, but they did not carry out full-frontal charges. They were dual armed, bow and lance. If the enemy closed ranks to protect against a potential charge, they used bows. Similarly they used the cavalry more for flank envelopment, not as a frontal shock force. Therefore their tactical doctrines suggest they did not consider it wise to chuck heavy cavalry at an opponent who was not frail.

A full charge from knight was devastating, and commanders went to lengths to minimise the chances of receiving such a charge. However, against quality infantry - pikes or not - a frontal charge was also very painful for the knights. Historically, virtually every time knights charged heavy infantry it was done because the enemy was considered to be low quality, disordered or close to rout.