Holding high ground is nice, but it's not always available on the battlefield you end up in, so this is what I do. I just have all forces follow me and I ride slowly forward with my forces, then, once the Khergits or Bandits charge, I stick to one main tactic. I use a mix of ground troops and mounted troops, so I order a full out charge, as for me, I carry a jousting lance for my polearm to couch with (It's superior reach comes in real handy here). The big thing to do is couch their horses. When you couch a horse, it usually won't reset your weapon so you can couch multiple horses with ease, especially if you use a faster mount.
So, I just mow through horses one by one, and even beat Khergit Lancers who also couch, since the jousting lance has superior range to their weapons. When their horses go down, they are nothing but fodder, both the Khergits and Steppe Bandits, and my troops will just mow right through them. I should also note, I use higher difficulty damage settings, so no, I do not do this on easy mode, I do it on higher damage to me and my troops, and a higher ai battle rating, alongside the battle size increasing mod, so this also works with far far more things fighting at once.
If you don't use a mount, then I suggest a poleaxe. The Poleaxe rapes mounted troops big time, if you get a swing in while they are charging you, it will usually one shot the horse if you have decent enough stats, which point they are cannon fodder.