@ Wakboth
I don't claim to be an expert, but I think you're wrong about how battle damage is calculated. Battle is all based off of a die roll type of thing. I believe the way it works is that the computer looks at what the attack and defense are, 2 and 3 respectively in this case, and builds a 5 sided die, in the computer sense that is. Lets say that 1 and 2 are assigned to the horseman and 3-5 are assigned to the spearman. It then "rolls" this 5 sided die and if it lands on one or two, the spearman takes damage. If it lands on 3-5, the horseman takes damage. So, the spearman has greater odds of hitting the horseman, but it is completely random, which is why a warrior can damage a modern armor, even though its highly unlikely.
The reason I say this is simple. If your way of doing it was how damage was calculated, then how could a spearman ever damage a modern armor?
As far as I know, the only benefits of having a higher experience level is the hps the unit has and its chance to retreat if its fast.
About your edit, that makes even less sense. If you claim that a 3 def would cause 3 hp damage and a 2 off would cause 2 damage, then with a regular horseman, after the firts battle, the spearman would be down 2 hp to either one or two, depending on if it was regular or veteran, and the horseman would be dead.
No offense intended by this, just wanted to put that out there. If somebody knows for a fact how this works, please let us know.
EDIT: Fast units retreating used to be gauranteed when Civ3 first came out but was modified in one of the patches or with PTW. Now it is a percentage. Default is as Oystein said: 34%, 50%, 58% and 66%.
So, if you get to the one hp left situation, you will either win or lose but you won't retreat. If the defender still has more than one, you get a die roll based of of the attackers exp. level. If you have a regular horseman, the die will be 1-50 are retreat and 51-100 are stay and fight. If they are veteran, 1-58 are retreat and 59-100 are stay and fight.