Well, you contradict yourself. You say you dismount the horse because it is very risky to use after the moment that it is heavily damaged. So if one of your opponent tries to ride it, he/she get the disadvantage instead. 
No it seems like a contradiction, but it isn't.
For example: that's could be an advantage for that person and a disadvantage for me, because I have no ranged weapons. It depends on the situation:
On an average battle there are several archers or throwers gunning for me when i do ride-by's, so trying that with a wounded steppe horse is very dangerous. So dismounting is often a prudent move. And killing the wounded horse makes sense if you are heavily outnumbered, for example, because there's a reasonable chance an enemy gets to use my horse against me.
When my team is winning, there is often no need to dismount when my horse is wounded, because there is enough 'safe ground' where i can ride without risking getting killed during the 'stun' period when my horse dies. It's all about positioning and keeping track of friendlies and enemies and minimizing risk accordingly.
Currently sitting at 7/7 still have to level a bit, however I am having a lot of trouble with my courser. The horse simply dies way too easily, when I charge an archer and he notices it (not a little sound) and he hits me charging him head on he can oneshot my courser.
The courser dies so fast because you are charging straight into those arrows / bolts / thrown weapons. Speed bonus is a big factor in cRPG. If you move away from the projectile, you'll notice that it'll deal much less damage. So try to be aware of all the ranged classes that are aware of you and simply avoid.
Another trick you can try: slow down. Instead of galloping at full speed when you approach an enemy from behind, you can slow down to a canter. That makes a lot less noise.
Also, use water to mute the hooves sound when there is water available (only on a few maps, sadly). Staying on the water's edge allows you to go full speed without making much sound at all.
So my only option is to be zoned and move away from any wary archer, which in a full battle is near impossible.
It's hard, but not impossible. Try laying low the first minute or two and taking more risks once the amount of (aware) ranged classes gets less.
You must think of cav as a support class. We cannot engage enemies directly, but we must rely on our teammates to disrupt and distract enemies, so we can sneak in from behind and hit them while they are busy (or at least focused) on your team's infantry. Or even other cav. Get out before they shoot you.
I would not recommend going 8 riding. It is not going to increase your survivability on horse much. Riding only improves your maximum speed, turning speed and accelleration... not horse hitpoints or anything like that.
Instead, try a different horse. Courser drives like a bus. Or perhaps like a drag racer. Great in straight lines and good for chasing other cav, but very hard to attack (aware and skilled) infantry with.
Perhaps a Destrier is a good horse for you. Or one of the armoured horses. They only need riding 5, by the way.
