Yes it is true and ironic considering the premise of this thread - the AI never builds horse in the early game when they are most effective. All the more so as the AI is programmed to rush the human, apparently when you plop down a 3rd city, from what I can gather from these boards. That is fine, except that part of the rush program should be "research HBR"!
However the AI can spam fairly massive classical armies if they are determined to attack you. I had Arabia spawn about 10 spearmen backed by 5 archers plus 1 swordsman and a catapult in a rush on a frontier city. Luckily my Horsemen of the Apocalypse army (3 + 3 Egyptian chariot archers) had been posted on sentry duty after having bum rushed the English out of the gate, so I saw the approaching Arabian army even before they declared on me. They lost the element of surprise as I hastily concentrated the horse army, + 2 warriors and an archer lying around, about the target 4 pop city. Plus a GG from the English war. I can say that spearmen in this quantity inhibited the use of the horsemen, and the defense relied mainly on the ranged units + the city, plus the lucky coincidence that I had opened up my first iron mine (2 iron only though) and had money in the bank, and was able to upgrade the warriors to swords just in time - without those I might have actually lost. The horsemen meanwhile were largely relegated to flank duty picking off weakened units, plus the catapult that the AI stupidly placed in the first assault wave. It was a long bloody battle before I eventually prevailed with the loss of 1 horseman, 1 chariot archer ( meanwhile I build another horseman + swordsman and brought them to the front, that's how long the battle lasted. Plus using insta-heal promotions). All this on King only, so this was not the result of some Diety AI overkill.
I never saw an AI GG out of all of this, in fact I almost never see AI GGs. I did see that Arabia had advanced down the Honor SP branch, as his units had the 15% adjacency bonus, so that was smart prep at least. But the AI doesn't withdraw heavily wounded units from the front lines to fight again later, allowing me to kill them in the next round. But the AI did tend to place archers behind (or at the flanks, where they were however vulnerable to my horsemen) the massed ranks of spear.
But strategically, yes, the AI is lame early game: either it attempts a (horseless) early rush, or it builds no defensive military and sits like a patsy for your Apocalypse army to walk in. This is crucial as he game is half won when you clear your continent, opening up a long era of massive peaceful expansion in prep for the endgame. I actually did this with ...Ghandi
...on a large map on a huge continent shared with the Babs (1st down) Romans (2nd) Arabs (3rd) and Egyptians (last). Bing bang boom. Only one to field any army was Arabia, a spear and a few warriors was all. the rest just some ranged units, the Romans, zilch. You'd think they'd get the hint after I mercilessly rolled Babylon early on. Perhaps the AI is programmed to think: "human = Ghandi = peaceful culture player, can relax"? Well fooled them
In which case this makes Ghandi the deadliest of early game threats in human hands.
And perhaps game over on Pangaea, which I therefore never play in Civ and have not yet played in CivV.
Immortal/Deity is no different to Emperor and below in this respect. Across half a dozen or more games at the highest two levels I actually don't think I've ever seen an AI Horseman. I occasionally see Chariots (especially if it's Egypt), but that's about it. The AI currently seems to be biased against building them (or researching HBR), for whatever odd reason.
Immortal/Deity is really only different in the sense that sometimes the AI will randomly declare war on you around turn 20 when you have no defences whatsoever and no chance to counter their dozens of free units. Apart from this silly occurrence every now and then, the Horseman rush strategy still works well right up to the top levels. The sheer ease with which one can eliminate civs even on Deity with a few Horseman units is indeed rather sickening.
It's a combination of an overpowered unit and an abysmal strategic AI - one that never really builds Horse units, hardly builds Spearmen, sends its Archers to the frontlines to die, and leaves its cities almost entirely undefended. There's no challenge even on the highest levels at the moment, as long as you survive the initial setup stage without the AI dogpiling you with all its free units. If you get past those first few dozen turns or so on Deity, you're pretty much set for a win with the Horseman-rush "strategy".
toned down, and only 3 
; building them would still have merit, but they wouldn't be able to sweep up an entire continent in a few dozen turns.
