There is a mention of horn armor that I remembered from the Greater Annals of Cologne, which describes a conflict between the Holy Roman Emperor Henry V and the city of Cologne during the Investiture Controversy.

In the meanwhile the cavaliers of both sides had a free field and rode against one another as if they were taking part in a spectacle; but when a great cloud of arrows came showering in from the side of the Cologne people the knights of the enemy fell dead or wounded. There was in the emperor’s army a corps whose armor was made of horn and so could not be pierced by iron. When these removed their armor, however, in order to get a little air, for it was very hot, they were immediately covered with arrows, and all but six fell on the spot.

As a warning, what I'm writing is really speculation based on my personal background knowledge of armour. I'm not a historian, and in any case, horn armour is not something that appears in many historical records.

Now, the nature of horn, and the few uses where I've actually heard about horn being used in armour, lend me to believe that this armour was likely scale or perhaps lamellar, though lamellar was not quite common during Germany in the 12th century. It could have also involved horn plates attached to mail links (steel or iron plates were sometime affixed in a similar fashion). If I had to take a guess, though, I would probably assume it to be scale, perhaps worn on top of chainmail.

Now, that account does give good credit to the armour, which is described as not being able to be pierced by iron. It is my assumption that the author was referring to its good showing against enemy arrows, as horn, while strong, has no qualities that would make it any better than iron or steel in terms of invulnerability to penetration. A lance can go through scales of horn, I have no doubt. Arrows, however, would have a tough time against it - particularly if the armour was worn over a backing (at least a gambeson, which was a form of padded jacket, and perhaps over chainmail as well). However, it is worth noting that arrows in general had a tough time against armour. There are famous accounts from the Crusades of knights who would have been wearing plain, old-fashioned chainmail on top of padded garments surviving hails of arrows and continuing to fight looking like pincushions. Scale or lamellar made with iron or steel is similarly effective, and even lamellar made with leather can perform quite well (the Mongols and Japanese used such armour). Plate is nearly invulnerable (except to very heavy crossbows), but full-plate armour wasn't a thing in the 12th century.

Crossbows can have a good go at armour, but 12th century crossbows weren't quite as powerful as some of the ones that would come a bit later. In general, a knight surviving arrow fire would not be rare.

However, that does leave a conundrum - the author describes our horn-clad knights surviving the arrows (until they removed their armour) whilst knights weren't all so lucky. How is this the case?

Well, a standard knight would have been wearing chainmail in this time period, over padding. It is my speculation is that Henry V's horn-clad soldiers were wearing some form of horn armour over chainmail. Chainmail is very good at providing near-universal coverage, whilst, say, chest and back armour made from horn scales probably wouldn't add too much to the overall weight of the soldier (at least not much compared to the mail itself, which was quite heavy). So this would provide more protection against arrows. However, I'm not really convinced that this was some magical arrow-stopping technology, and the fact that the members of this corps felt at liberty to take off their armour tells me that they might have been hanging back a bit from the main battle, and were a bit overconfident as a result. Plenty of knights without horn armour probably survived just fine, but they don't really get much attention. I'm not too convinced that it would provide significantly more anti-arrow protection than mail itself, and it the fact that horn armour is almost never mentioned throughout the Middle Ages, despite the fact that people did have access to horn, would support that.

Personally, my conclusion is that this horn armour was probably just there mainly for show, and the people wearing it probably happened to be hanging a bit further back when that shower of arrows from Cologne occurred. To answer your question as to who was wearing it, they were probably a group of knights. Horn by itself would not have been better than mail. Horn on top of mail would have perhaps been a bit of an improvement over base mail, but not enough to justify its widespread use.