One of the great misconceptions of history is the horned helmets of vikings. This is in fact untrue, they didn't have horned helmets. But horned helmets were a thing thousands of years before the vikings. And have been used from time to time.
What reasons would an army have for putting horns or antlers on their helmets? What are the benefits that they apply? What are the cons?
Horns and other decorations on helmets served many different purposes over the centuries.
The initial reason for decorating the helmet is to make the wearer look larger and more impressive and to provide a psychological boost against the enemy. Large horsehair crests on Mycenaean helmets were meant to inspire terror. A small incident in the Iliad has Hector frightening his son by entering a room still wearing his helmet, as probably the best known example.
Later the use of decorations was to provide identification of leaders in battle. In the Roman legions centurions wore traverse crests on their helmets to identify them in the field. Japanese leader's helmets from the Age of War could have fantastic decorations to mark high ranking leadership.
Centurion
Samurai leader's armour
Clear identification of the leadership is the most obvious benefit from decorating the helmet, but the extra weight could unbalance the helmet, make it difficult to wear or to user to move their heads and provide places to catch an enemy blade. A "normal" helmet provides smooth surfaces to provide a glancing blow to a blade or bludgeon, rather than things to trap or redirect blades, potentially giving the enemy a means of providing a damaging blow. Of course, this also provides a means for the enemy to identify the leadership, and if they focus their attacks on eliminating identified leaders you could be in some trouble.
In general, helmet decorations are as large as practical, and reflect the role of the wearer. A Roman centurion's transverse crest is not so large that it affects his performance in the field, since he is embedded with the troops he leads. A Japanese general has a much more elaborate helmet, because in general, he will not be directly engaged in combat, but rather sitting back far enough to observe and direct the action.
All of the animals whose heads are adorned by large horns, are strong and dangerous creatures. Especially in pre-gunpowder ages, the possession of some dead animals' horns by a human was proof of the strength and skill of that human.
It is a status symbol, but it is also proof that its owner's status is deserved.
The horns trumpet... "Look what I killed!"
In close combat situations, a headbutt with a spiked (as opposed to horned) helmet has the ability to debilitate the opponent, and in some rare cases, kill him.
Note that I am talking about spiked helmet. Of course you are free to shape the spikes as horns, but I would wager the best shape for such a helmet (designed for goring the opponent) would be to have an 8 inch long spike on the forehead part of the helmet, facing horizontally forward (akin to a unicorn's horn).
Helmets with animal-horn fashion protuberances were meant to shake the self confidence and gallantry of the opponent make him psychologically weaker.
So, a lot of people have already answered talking about various reasons like looking impressive, showing rank, bragging about hunting (Early Greeks did a similar thing making helmets out of boar tusks)impersonating animals/monsters or having horns for ceremonial reasons (like the Celts).
But mainly I'm just commenting to let you know that the misconception about Viking helmets being horned is down to flaws in Victorian Archaeology, not Skyrim. Sorry if I'm repeating anyone! Just thought you should know!
Also, in a fantasy scenario, an uncivilized culture may use horned helmets as horns for similar purposes as animals that have horns (i.e. fighting for mates). Having horns on your helmet can get in the way though/ get caught on things/ be used as handles to shake your head about so not always practical in battle!
We often depict Vikings with horned helmets because it makes them look more intimidating - wouldn't it be reasonable to suppose, then, that an army might put horns on their helmets for exactly that purpose? A scared enemy is a weakened enemy.
Alternatively, I could imagine that branching horns - like a stag's - could serve a battle purpose by catching an opponent's sword on the rare occasion that an attacker chose to swing downward at the soldier's head.
Alright I haven't seen people explain the biggest problem with horned helmets. You know what happens when someone hits one of those horns very hard with their weapon?It's like someone decided to jump and hang on said horn. You get a tremendous pull to the side.
Now if you're lucky that means your helmet comes off. Not a great thing in battle. Now if you're not as lucky, then it means the helmet will cut into your shoulder and neck. But if you're really unlucky you simply break your neck. Actually that's not so much unlucky as that it's likely.
So that's why frontline troops never wore horned helmets. Sure there's probably some rare exception but by and large, none. As vaguely mentioned above, horned helmets are a relatively modern invention. Operas like those of Wagner about Germanic folk tales are a likely origin. They needed them to look imposing from a distance and preferably relatively cheap. Animal horns was an easy way to get that.
Reasons to use them have been mentioned extensively in other questions. You look imposing. You believe you invoke the animal's spirit for strength or protection. Identification with ir without the associated fear that produces. In reality you want a helmet to be domed and smooth. That way a blow has a good chance of glancing off relatively harmlessly. And not get stuck behind a horn, breaking your neck.
