Tribes of Midgard

When your Viking dude reaches level 3, they gain the ability to summon a horse to ride. This horse is only for riding. The moment you get off the horse, whether to collect resources or fight enemies, the horse vanishes back into the aether. The horse does not get involved in combat. This is a pitiful horse. Though you can get a cosmetic effect to turn them into giant chickens, which is cool.

The Longest Journey + Dreamfall + Dreamfall Chapters

The closest thing to a horse is the Arcadian elgwan, but they're pretty docile. Some puzzles involve spooking them into being a distraction but there's never a sense of anyone being in danger.

Day of the Tentacle

There is one horse in this game, owned by the Edison family of 18th Century. It can talk, which is probably a reference to the classic TV series Mr Ed, a reference that went completely over my head as a young British child but I am now familiar with as an older British adult. The horse is kind of rude to you, but you put it to sleep (actual sleep) and steal its teeth, which makes it less intimidating.

Jack Orlando: A Cinematic Adventure

You are warned about the horse in this game ahead of time, so you don't really get a chance to provoke it and it stays docile, happily eating oats. You do need the horseshoe lying nearby to commit hate crimes, but that's not actually the horse's fault in any way.

Sid Meier's Civilization IV + V + VI

Horses (collectively) are a resource in these games, used almost exclusively in the production of cavalry units. This does make them slightly more unnerving, though in all these cases they are being ridden by a soldier and not doing the attacking themselves. They can also be a source of Production and, sometimes, Food. In Civ 5, they also let you build a circus.

The Elder Scrolls IV: Oblivion + V: Skyrim

Horses can fight in this series, they just die very quickly or run off and leave you to fight alone, which is very true to life. In Oblivion you can ever get horse armour to help they stay alive for, like, 2 extra seconds before they die anyway. Shadowmere is better as in both games she/he (it seems to change) can do more damage than a regular horse and is effectively immortal, though in Skyrim you need to get them back from where you found them each time.

Then we have the Oblivion Unicorn. Fuck that unicorn, I mean seriously, to hell with that thing. This is the most realistic depiction of a horse I have ever seen in a video game, as it decides it hates you and tries its very best to murder you at the slightest provocation. Literally, even having your weapon raised is enough to put you on its hitlist. It has no understanding of mercy and even if it did, it would deny you it.

Terraria

Horses (along with a unicorn) are also mounts in this game, allowing the player to speed across the map. They can't attack by themselves but if taken to a high speed then they will do damage to enemies they make contact with along the way, which anyone who has been trampled by a runaway horse will tell you is completely accurate.