Initially while thay are still wild they should move around the map, maybe limited to the plains area in which they reside (or stay near a fesh water source), rather than remain static like the other resources. You should then be able to chase the herd using any unit toward your cities. Once they are inside a cities radius it depends what techs you researched as to how many horse you get to "harvest" for units per turn.

Rather than just reseaching Animal Husbandry to then have access to a certain amount of horses per turn, make it more incremental, have a few techs through the research tree relevant to getting more out of the horse resource you control.

So initially when you have researched no horse techs you get 0 horse even if the horse is passing through (or been chased by your units) to your cities radius of control. If you research, I dunno, the Lasoo, then you can capture one horse every five turns the herd is resident in one of your cities radius. Next tech might be Bareback Riding, and you get one horse every 3 turns and so on and so on. I don't know how many levels of reseach you'd have or how spaced out within the tech tree they should be. The last tech could be the Ranch tech when you can actually corral and stop the herd leaving your city radius or requiring units to keep them there. The ranch doesn't have to be connected to the rest of your city and therefore not necessarily be protected by the garrisoned unit or he cities defences, in fact I'd say you could even make sure that there is a one tile gap between your Ranch building and any other building in your city. The Stables tech could allow you to take a horse and make a War Horse after 5 turns of training.

Cavalry or any other horsed unit is a powerful unit and therefore it should require alot of investment to be able to employ them, and keep them protected.

If you have to move your units off to defend a city or your carvans (and you haven't research the Ranch), then you run the risk that the herd may be able to leave your city radius and head away meaning your supply of horse returns to 0 until you can herd them back again. Since the herds will only move around within a certain radius (plains or fresh water, no idea how many tiles big this area would be, I guess it would depend on map size as to how large or small an area they can roam) it would stop players from herding all horse back to their civ, but would still allow for some strategy regarding keeping control of them or taking control away again. Don't forget that a cities radius gets bigger and bigger so as a city gows it'll become easier to have horse in your cities radius.

I dunno if this is actually going to be a workable idea really. Certainly it allows for some strategy regarding cutting enemies off from their horse resource so as to starve them of those units, but hopefully players will learn to protect the horse resource fiercely and not allow this.

Not totally thought it through but  I'm sure people cleverer than me could refine the idea if it is something that would add fun and choice to the game.