Because Khuzait have such a snowball problem, I've spent about two thousand game-days fighting them exclusively, compared to only a couple hundred game-days fighting other factions. I found that the tactics I developed to counter the Khuzait didn't work well when facing Vlandians, so I had to start developing new ones. The latter are still WIP, but versus Khuzaits, this works:
If the map gives me enough room, I'll put my archers in loose formation and tell them to watch the front-left (giving archers a watch direction is the most important part of fighting Khuzaits), and I put my infantry in shield wall to the right of the archers. My companions (all horse archers) will be a few meters behind the archers, while the rest of my horse archers will be on the right flank. Cavalry is on left flank.
If the map doesn't give me enough room for that, then I have my infantry shield-wall about two meters behind the archers, with both archers and infantry ordered to watch the same direction (so that the infantry line does not rotate into the non-rotating archer line, blocking their shots). Both lines will also have less of a diagonal angle in this case, facing more toward the main enemy force and less to the 10/11 o'clock position. This is because the infantry should be be already aligned with the enemy battle-line before charging, and if they're close behind the archers, they can't change alignment without getting in the archers' way.
Either way, Khuzaits will almost always suicide their horse archers on my left side at the beginning, which is why I like to face my archers front-left. With their line diagonal like this, relative to the enemy formation, they can shoot the enemy horse archers to my left and also shoot the main enemy force to the front, all without having to reposition the line (which would waste time better spent shooting). After my archers have loosed a couple volleys at the enemy horse archers, I tell my cavalry to charge, and I join them. At this point, the enemy horse archers retreat, and we cut most of them down. When we get too close to the enemy archers, I break off the attack, telling my cavalry to join me as I fall back to my battle-line.
By now, the enemy usually will advance their main battle-line, and my crossbowmen are doing most of the work. I take my horse archers (companions, too, unless the enemy has a lot of cavalry, in which case it's too dangerous for companions) to flank the enemy from my right (their left); this isn't completely ideal, because their shields are facing us, but it does let my horse archers shoot while we widely circle the enemy formation.
We'll end up directly behind them, if the enemy cavalry don't interfere, but after being pelted for a bit, the latter usually charge my horse archers. So I order them to fall back to my battle-line's left flank, and I engage the enemy cavalry as a lone lancer. Khuzait cavalry (unlike Vlandian cavalry) aren't usually too difficult for a reasonably-skilled player to take out by himself. The main challenge here isn't killing them without being hit back, but rather keeping track of the big picture while also spearing horsemen. (When facing Vlandian cavalry, on the other hand, each enemy lancer is himself a dangerous threat.)
When the main enemy force gets close enough to my battle-line, I tell my infantry to charge, and my cavalry to flank wide left. If necessary, I tell the archers to fall back, but I need to remember to tell them to stop after a few seconds of this, or else they may retreat off the battlefield altogether.
Although my cavalry are flanking to the enemy's right, I avoid charging my cavalry into the enemy infantry unless it's an emergency. Rather, I prefer to bring them around the back and join them to take out the enemy archers. This can be hard on the cavalry, so I pay attention to how much heat they're taking and back them off if I have to, assuming I have the option (if it's a very tough battle, I may have no choice but to keep pressing the archers with my cavalry, despite them taking heavy losses from it).
When I join my cavalry in the archer-slaying, I have a tactic of approaching their line directly from the side, so that only one archer has a clear shot at me until I've hit him. I'll then tightly weave back and forth through the formation at high speed, stabbing two or three more archers in the head by the time I reach the other end of it. (This wants a horse with a high Charge stat, or else you'll slow down too much after bumping into one or two archers). Then I go evasive, 'beaming' them counter-clockwise to show them my shield, widely spiraling outward to increase the distance.
Any arrows they shoot at me as I circle them in this defensive manner are arrows not hitting my men, and with my speed and shield, I can handle a few arrows better than my stationary archers can. And if the enemy archers give up shooting at me, well, then I repeat the maneuver, taking another few of them out, and again disrupting them & drawing their attention.
That pretty much sums it up. There's a little bit of dynamic-ness to it, but mostly the battles follow the same loose pattern when you have a setup like mine, use my tactics, and are facing Khuzait. This is all assuming you're playing on max difficulty.