If they have a long spear/lance yes, you dont have much of a chance - But, if they have two handed or a shortspear, I can usually get a stab in on the horse with my Long Espada, this works very well.
Even if the cav has a lance/long spear, you can still attack him. If you have a buddy, and he is standing behinde you, ready to stab, you can block the cavs attack, and let your buddy stab - this works well too.
1. If you don't kill the horse, the rider will then kill you.
2. short spear on horseback? How often do you see those?
3. How many cavalry (proper ones) are going to try and kill you when there's someone waiting for them with a long pointy stick.
there's an animation when they are stunned tho, you'll know it when you do it.
There's a nasty little trick archers have now. Aim in about 90 degree angle sideways from the incomming shielder. Then, just before he clips in you, you quicly turn to the shielder and release the arrow. When you time it right, you bypass the shield and hit the shielder, even when he has his shield up.
Happened to me a few times now. Timing is crucial, if you do it too early you hit the shield and you're dead. Do it too late and you get bumped.