The ai no matter who they are favor horse units,pikes, elephants with a few siege weapons. Generally all AI leaders make stacks of doom (SoD's), even at peace time.
If they don't have an SoD when you war-dec them,
they will build one fairly fast. The AI is not smart with using its stacks(generally). But it makes up for it by committing all its city's to the war effort by building units. So it just looks likes its producing stacks out of thin air.
If your going for a calvary offensive stack. Don't slow it down with 1movement units. You just lost the advantage of using calvary if you do.
- Build A 20ish (in the very least) stack of corsairs/calvary to start with. make sure you can produce them at a fairly fast pace. Typically if I am calvary focused civ. I have in the very least 5 city's poping calvary every 4-5 turns (some city's faster, some city's slower). I play epic game speed. Generally its quite a few more city's producing than that tho for me. If thats the way I am tech focused.
-Have a medic III in at least one of the stacks. fast healing after a city raid = less time for the AI to catch up to your mounted units which have no defense bonuses other than terrain.
-Always try to end your stacks turn using a defensive terrain. Such as forests,hills, or even better forested hills when on route to wherever. You will be amazed at how much of a difference this alone will help with survival of said stack. Again- you should never park your horses on a bare tile unless you absolutely have too. (no defense bonus applies to terrain as well? I have not done any testing or really payed attention. But it seemed to help, altho I changed a few other bad habits of mine around the same time frame. /shrug)
-use spies to put city's in revolt before attacking them. They move fairly well make sure you have the points and a decent number of spies before you start the war. Another thing its a good idea to move and use your spies in groups of 2. Having a failed attempt at sending a city into revolt only slows you down. And its not uncommon to have failed attempts.
-Build city defense units if you plan on keeping city's. Don't move these in your main stacks. it only slows them down. Again loosing the obvious advantage of using mounted units.
Of course it helps to specialize your research. If you plan on using Calvary as offensive units. Its a good idea to really focus your researching to maximize their window of opportunity.
On a good note the AI does not beeline rifling normally. And if your fast enough by the time they do. They simply can't produce enough to stop ya.
I know some of this is fairly common knowledge. This is just stuff from my personal experience. Or how I perceive the Ai's habits. Hope some of it might help with some of your game/games.
Edit: I generally play on Noble, Epic speed. Anything else just becomes to much to keep my attention for long. To much micro-managing. And I noticed you were complaining about your mounted units. So thats why I focused my reply towards using them.
And like the poster below me and a few others have noted. If your just starting the war and you don't have SoD of calvary while your enemy has riflemen. Then forget it. the window of opportunity closed.
Reasons for edits today. Just fixing a typo or 2 that I happened to notice.