It seems horses are a resource that works similarly to metal or crystal - you harvest a tile with "wild horses" on it and if you lose the city with the tile, you can't make mounted units. But there's no reason that, once you tame some horses, you can't take them elsewhere to breed and raise horses in other cities.
In real history, when cultures came into contact each would start to adopt the domesticated animals and plants the other used. In this way, species would spread far beyond where they were naturally found as humans bring them with them. This was the case with horses - they were first domesticated in Asia, and spread throughout the "old world" because its cultures were in mutual contact. But in the Americas, horses were unknown in many places until the Europeans introduced them - and having horses gave them a huge advantage in wars with Native Americans.
This is the difference betwen ore and "renewable resources" like horses, wheat, and honey bees (all examples which are in the game now). Once you discover them, you don't depend on one place for a supply, but the first to find them still has an advantage.
So I suggest that these work a little differently in the game. Once you first find a tile with a "living resource" like this, you build a structure (stables in the case if horses) to harvest it. But once you have one such building, you can then build it in other cities which don't have a special resource tile. Thus, once you have one wheat farm on a tile with wild wheat, for example, you could export seeds and build wheat farms in other cities. If you lose the city with the wild wheat, you can still build wheat farms so long as you have at least one city with one. Same with horses, honey bees etc.
This would be subject to the same rules that other resources work with - for example, if a city is under siege it can't import resources unless it has a native source, so a city without a wild horses tile can't build stables, even if you stables, if it's under siege. Likewise if your only city with stables is besieged, it can't export its resources so your other cities can't build stables.
These resources can be introduced from one kingdom to another through the trade system - if one civ has stables it could make a deal in which it gives a breeding stock of horses to another civ so they could build stables in their cities. You could also conquer a city with the appropriate building (stables, wheat farm, apiary) to gain access to a resource like this.
On the side, it would be very appropriate if stables were a food consuming building, just like housing. This represents the way that feeding and raising horses for mounted armies is a major logistical/economic concern since the animals eat more than the people do. It adds some strategic decision-making, so players won't necessarily build a stable in every city, and adding cavalry to their armies is an undertaking in itself that requires specific resources (food surplus).
These things would also apply to other kinds of creature you can tame, if the game has them. I don't know if the game will have warriors riding fantastic monsters, but mounts or war beasts that aren't horses don't have to be imaginary creatures - wouldn't it be cool to have ELEPHANTS in the game?
