Just a possibility, may or may not be to complex:
Cavalry pretty much was a shock unit. Devastating on the attack, weak on the defense. And also weak once that first attack came to a halt within enemy lines if these didn't break. Of course this has changed a little in colonial times, as cavalry no longer was as unstoppable without pikes or similar heavy close combat weapons, but infantry no longer fought in just as deep formations anymore, giving cavalry a higher chance of not getting stuck.
On the other hand, cavalry attacks always had and kept a very strong psychological element. a full unit of big horses charging at your line at full speed must have been a terrifying sight to behold, especially when you had no real means to defend yourseld (which against a musket armed unit could just mean an attack from the side, were almost no musqueteer still had time to bring his weapon to bear before the cavalry crashed into the unit.
Now, instead of just cavalry > infantry in the open. Why not differentiate who attacks and defends? It must have been pretty rare with the cavalry units speed, but a cavalry unit caught in the open by an infantry unit will be a sitting duck. If there is not enough space for building up momentum for a counterattack, the cavalry unit faces the option of fleeing and hoping for taking not too much casualities, or be wiped out by the numerically superior and better armed infantry (remember, shooting from horses backs was only really possible with short weapons like pistols, because of the instability of the "horse" platform)
This will of course lower the value of the cavalry unit. For one, the cavalry should be fast enough to dictate the engagement for one, meaning as long as a player does NOT forget to use his cavalry the way its meant to be, not to hold lines or guard things, but as a mobile reserve, the cavalry will always be in the better position. It will mean that cavalry and infantry get their "roles" even outside of terrain considerations.
Also, you could add a psychological effect to a cavalry charge. Which could either mean that cavalry gets an additional bonus on the attack (which, given you want to go so much into detail, should be higher for charges to the side or rear of infantry units... which is something cavalry is especially good at). Or, if you add psychology, that a cavalry charge can easely break an infantry units moral and force them to flee even before the cavalry unit makes contact (which means an ugly slaughter among the infantry men should the cavalry unit decide to run them down).
As for artillery, one important aspect to artillery is field of fire and time to turn the weapon. Which in turn means artillery needs to be setup at the right spot from the start to be really useful.
Find the right position for your artillery, and it can have just as much a devastating effect as a cavalry charge from the side (which is something SOME tried to achieve, with artillery firing sideways into the not so deep but very wide lines of the infantry in the day of musket warfare).
Misjudge the right position, and you will have to move the artillery during the fight which takes A LOT of time (most artillery should be slow to move, not because of the actual transport, but mostly setup time, and moving into position by human power for the last few meters)... or your artillery will not do much during the fight.
A more limited field of fire, slow movement, maybe a longer aim time (compared to muskets) could offset long range, devastating damage to whole units, and the sheer psychological effect of being shot at from units you cannot reach with your weapons, and seeing whole ranks of soldiers being horribly killed by a cannon ball.
Artillery should take some preparation time to adjust to a new target, but when aimed in, should do heavy damage to the targeted unit. On the other hand, because of that time it takes to adjust the aim of cannons, moving cavalry should be a harder target to hit for artillery (whereas a musqueteer unit should have a devastating effect on a cavalry unit charging from the front, if the musqeteers are well trained and can keep their cool).
Just some random ideas
But i dont like attack/defense in that sense. If two cavalry units are both standing on a prairie, and one "attacks" the other (since it's turn-based) why is that one much stronger? This is why I have three distinct scenarios:
Its both simple physics and a question of human psychology. And lastly, having the tactical advantage.
The attacker chooses were and when to attack. He can control the fight to some extent. Units ALWAYS have way more lag to their reaction than single soldiers. If the attacking cavalry manages to attack from the side or rear (maybe because nobody in unit being attacked watched the side or rear often enough to see the attacking unit before it was already to late to reorganize the unit), the defending unit has a HUGE disadvantage.
Also, the soldier in the defending unit might not be prepared (yet) for a fight. The attacking cavalrymen are.
Simple physics dictate that the soldier with more momentum has an advantage. His blows, if using the momentum, have way more power. The defender of course CAN use the same momentum against the attacker, but chances are the defender will have less time to judge the right attack vector, while the attacker has already aimed for his target and formed an attack vector way before that.
Momentum is the SINGLE BIGGEST weapon in a cavalry attack. Without momentum, the cavalrymen can use the additional heigh for more devastating blows given the right weapons. At the same time, they can be easely dragged from their horses by numericaly superior infantrymen.
Psychology. If a cavalryman charges you with full speed, you will need a hell lot of nerves to stand there to take the attack at full force. Even if you sit on horse, the psychological effect is still there. You KNOW the enemy has the advantage. You KNOW how devastating a cavalry charge is (you do this yourself as cavalry all the time).
Lets not get into the psychology of their mounts. Whith even the best trained horse loosing their cool at times.
Then, last but not least, cavalry would dismount on the defense and fight on foot, BECAUSE only this way they could use some weapons, like muskets, or later rifles and machine guns, to full effect. And in the defense, a musket line oriented at the attacker still is better than a bunch of mounted soldier only being able to use their pistols and else waiting for the clash to use their swords and sabers. On horses that certainly are getting just as nervous as their riders as the enemy attack approaches.
Oh, and before we forget. Some cavalry was still using the spear or a lighter form of lance until pretty much the end of cavalry units. Now, this weapons is only of use to cavalry on the charge. Without the grounded stance infantry has and the ability to plant the spear in the ground, its useless as an anti-cavalry weapon. Unless the cavalry dismounts. Even then, different types of spears being used, and the cavalry now charges an infantry unit, just a very small and badly trained one (as most of their training was fighting on horseback, not on foot).