Quote:
"Now his wrath (Gwindor's, that is) was kindled to madness, and he leapt forth on horseback, and many riders with him: and they pursued the heralds and slew them, and drove deep on into the host."
-The Silmarillion, Chapter 20
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Seems to imply a cavalry charge - specifically the classic 'wedge', as they 'drove deep' into the enemy. But does it? Possibly the reason they managed to 'drive deep' was not that they had trained cavalry but that the enemy simply weren't expecting Elves to charge into them on horseback at all - they didn't know how to respond, & just ran away. An army that expects cavalry to be used by their opponents usually has plans in place to deal with it.
Another thing to take into account is that cavalry have to be trained - its not just a matter of sticking a bunch of guys on horseback & sending them charging off in the general direction of the enemy. You also need plenty of horses & fodder. Aristocratic Elves had horses as we've seen, but we don't know if they fought on horseback - Fingolfin rode to Angband to challenge Morgoth, but he dismounted & fought him on foot, & generally we hear of Elven armies 'marching up' to battle. Its as much a matter of what means the Elves had to hand (how many horses did they have access to?) & what tactics they had developed. Finally, you can't ignore the Elves 'embalming' tendencies & that generally speaking innovation was anathema to them. If traditionally they had fought on foot then there's very little likelihood that they would decide to try something new.