I wouldn't mind if I could mod in an upgrade for the stable unit to bump it up from +0.2 to +0.5 a season, but I can't even begin to figure out the modding mechanics.
Go to CoreImprovements.XML (it's in data\English\Core Improvements), search for the Stable (make sure it's the one that produces horses; you should a set of GameModifier tags that include a reference to horses), and make two copies of it in a new text file. Add
<UpgradesToImprovement>BetterStable</UpgradesToImprovement><UpgradeTier>1</UpgradeTier>
to one of the Stable entries, and change the internal name of the other Stable entry to BetterStable (you can pick any name you want, I'm just using this as an example name). This should then look like
-<ImprovementType InternalName="BetterStable">
instead of
-<ImprovementType InternalName="Stable">
Then find the portion of the XML for the BetterStable that says
Code: xml
- -<GameModifier><ModType>Resource</ModType><Attribute>Horses</Attribute><span style="background-color: #99cc00;"><Value>0.2</Value></span><PerTurn>1</PerTurn><Provides>+1 Horse per 5 Seasons</Provides></GameModifier>
and change the part that says <Value>0.2</Value> to reflect the production rate you wanted (e.g. 0.5, if you want one horse per two turns). You might also want to change the <Provides>...</Provides> text to reflect your changes. You should probably also add <UpgradeTier>2</UpgradeTier> to the BetterStable entry; the <UpgradesToImprovement> and <UpgradeTier> tags are found right after the <PreferredTerrain> tag in the Air Shrine entry, so you might put them at roughly that point in the Stable/BetterStable entries. Save this file in your LegendaryHeroes\Mods directory (which should be in My Documents\My Games, if you used the default install path), enable mods in game, restart the game to allow the changes to take effect, and you should have your enhanced stable available for use in game.
Another thing you might try is to see if you can change stables over to provide only X horses total (by changing <PerTurn>1</PerTurn> to <PerTurn>0</PerTurn>), although you'd then need to make your mounts increase unit wages by one horse per figure per turn (or some fraction of a horse per turn, if you wanted). This way, you could use the available horse resources as a cap on the number of mounted units you could field rather than having the ability to support a theoretically infinite number of mounted units off of a single stable, given sufficient time to produce mounts. Improvements to the Stable and adding additional Stables would then be the means by which your mounted army could be increased. However, it would probably take a bit of experimentation before you found a number of mounts per stable (or improvement thereof) which you were satisfied with, and I personally don't know how to add horses as wages to a mounted unit.
I'd suggest that if you wanted to do either of these things and ran into trouble with it, you should ask over in the Modding Help thread in the LH Modding subforum.