Horses are less vulnerable to traumatic brain injury than we are. A lot less. In fact, brain injuries are vanishingly rare in horses.
Why? The shape of their skull acts like a crumple zone...or, really, a built in helmet. Horses can hit their head very hard and not do any damage to their brain (which is also smaller than ours and rather less complex).
Head injuries in horses, thus, generally don't affect the brain.
However, a cut to the head - just like a cut to the human head - will bleed copiously. A cut above the eye can look particularly bad...and can also make the horse panic because it can't see properly. It looks worse than it is - once cleaned up, the torrent of blood often comes from a small slash that may not even need stitches. (I do, however, know a horse who cut his eyelid so badly he actually lost part of the inside - although you'd never know anything had happened).
Other head injuries in horses include:
1. Facial bone fractures. Yes, a horse can break its nose - but its bone, not cartilage. In some cases the horse may need surgery. I once knew a horse with a broken nose - the injury was quite visible, but didn't affect his breathing or usefulness as a riding horse.
2. Tongue lacerations. Tongue injuries generally heal well, even if untreated.
3. Ear lacerations. Horses' ears stick out. I also know a horse with a permanent notch in one ear, presumably from an injury. Severe ear wounds can cause the ear to curl up and may require a skin graft and to actually splint the ear.
4. Damage to the salivary gland and duct. You can tell when this has happened because saliva will pour from the wound. This ranges from minor damage to heal on its own to wounds so severe that one of the glands has to be destroyed (horses manage fine with only one).
5. Lower jaw fracture. These generally have to be wired or plated. But fortunately, they're pretty rare.
6. Nerve damage. I've actually known two horses with nerve damage caused by head injuries. One only had full feeling in one side of his mouth - which did cause problems when he was ridden, although the rider was able to compensate. (He was an English horse in England - in this country, I'd recommend that a horse with an injury like that be ridden mostly western and neck reined). The other...well, when she's relaxed, and when being ridden, her tongue lolls out of her mouth. She can eat and swallow normally, so its mostly a cosmetic problem.