This was just a poll regarding the initial 'disappearing' issue.
Horses moving around and acting realistically is a welcome addition, but since it would take a lot of coding, time to impliment, and there are very few people who care (including myself) I doubt it would be feasible at the moment. However I would most definately suggest this and / or support other people's suggestions regarding the issue, once the basics have been implimented in all fields, and the final 'touch ups' of the game are in progress..
As for horses disappearing more slowly, currently they would either disappear or NOT disappear. It is IMPOSSIBLE to get mount a horse if it is going to disappear, EVEN if you stand right next to it when the rider is killed. (you can test this by standing next to an enemy cavalry, and asking one of your troops to hack the rider off.)
Regarding Damien's suggestion-
I did think of a system however, which would actually have a 'bar' which would state how many horses are allowed to physically be present on the battlefield after the rider is killed.
Minimal digit is 0, maximum is unlimited. If the bar is set somewhere in between (example 10 horses), after the 11th rider is killed, the very FIRST horse which is ride-less will disappear, leaving 10 on the battlefield. (and so on subsequently)
So Damien, what I meant by 'option to stay' is basically some way of preventing the horse from disappearing, in YOUR case untill you get a chance to mount it. So if you still want to vote, you would fit under option 2, since its basically meaning the same thing..
However I think this would be more complicated to code in, and in my oppinion most of the people would either have maximum, or none.. (or adjust the bar whenever their horse gets killed, and resetting it back to 0 when they mount)