Moody Mount

A horse, dragon, dinosaur, or other creature that is being used as a mount has a mind of its own.... and doesn't like its rider. So it resists being saddled, doesn't take commands, tries and often succeeds in throwing the rider. Such animals are often black. They most likely started out fractious when being broken (indeed, broncos for rodeos are specially selected for the challenge they present), and this mount hasn't improved much with training. Don't expect bribes of food treats to work either; people foolish enough to offer a treat are likely to be bitten and/or kicked for their trouble.

He's the only horse we have left. His name is Earthquake, but we call him "Quake" for short. 'Cause that's what he makes all the stablehands do.

If such an animal is well-known to be temperamental, expect its name to reflect this. Characters in the know (stable hands or bystanders with expertise in handling such animals) will advise against riding the animal. Despite having such a reputation, a specific person may get good responses from the animal, and be much marveled at for doing so.

Frequently Played for Laughs. See also Horsing Around.

Examples of Moody Mount include:

Anime and Manga

Charizard in the early Pokémon anime.

Film -- Animated

Disney's Melody Time segment "Pecos Bill." See Folklore below.
In Spirit: Stallion of the Cimarron, the title character. Justified in that he was taken from the wild and treated harshly.
Maximus from Tangled won't let Flynn Rider ride him. Perhaps it has something to do with him being the Captain of the Guard's horse and Flynn being a wanted criminal.
Toothless of How to Train Your Dragon.

Film -- Live Action

Friar Tuck's donkey in Sword Of Sherwood Forest.
"Tornado" (the 2nd one) in The Mask of Zorro
Invoked in a Made for TV movie years ago. A boy and his bull, which was being raised for the rodeo bullriding circuit.
In Candleshoe, Priory (David Niven) rides a horse that is rather difficult to control. It eventually gallops off in mid conversation with Priory on it. It's not clear whether this is really a case of a Moody Mount, or if Priory is just that bad at horsemanship.

Lady St. Edmund: the Colonel's new horse must be even more spirited than Satan was.

Rashomon: The court officer claims that the bandit was thrown by the horse he stole from the samurai -- the bandit maintains that he fell out of the saddle because he was weakened by poisoned water.

Folklore

In the Tall Tale of Pecos Bill, the horse known as Widowmaker would let no one ride him but Bill. When Slue-Foot Sue, Bill's love, tried to ride Widowmaker, he took her for quite a trip - all the way to the Moon.

Literature

Ichabod Crane's borrowed horse Gunpowder in The Legend of Sleepy Hollow: "The animal he bestrode was a broken-down plow-horse, that had outlived almost everything but its viciousness."
About half the horses ridden by the heroes of Louis L'Amour's Westerns.
Stranger (ridden by The Hound) and Smiler (ridden by Theon) from A Song of Ice and Fire. Justified Trope since these are war mounts, trained for battle.
Discworld:
- In Going Postal, Moist von Lipwig rides one of these to another city to help save the postal system.
- Lt. Blouse's horse in Monstrous Regiment.
- And "You Bastard!" the camel in Pyramids.
Zeus, Theo's recalcitrant horse in the Fools' Guild Mysteries by Alan Gordon. Theo's little daughter Portia gets affectionate nuzzles, while everybody else risks life and limb just getting close to him, and even Theo has a touch-and-go relationship with him.
The Codex Alera gives us the Taurga, which try at every opportunity to dislodge, bite or kill their riders.
Counselors and Kings has a black stallion belonging to the Jordaini order, who despite being both the largest and the finest horse in their big stable typically was left in his stall. The beast was controllable most in the scenario "set the right direction and let him bolt like mad," and wooden hitching posts worked only until he'd get bored. Matteo rode this one when he meant business, after which he considered an unbroken horse not challenging. And upon reassignment named another aggressive mount after this one.

Some blasphemous groom had dubbed the horse "Cyric," and the name had stuck. The stallion was as volatile and possibly as crazed as the evil god whose name he bore.

In The Sharing Knife, Dag's horse Copperhead is habitually described as "evil", and won't allow anyone but Dag to care for him.
The tail end of Paladin of Souls reveals a vicious warhorse that Lord Illvin had been conciously attempting to ride to death. It is discovered that said horse is demon-ridden (which explained a great deal) and Ista tames it after a fashion with whipered threats of strangling it with it's own guts before feeding it to the gods.
Civan from Prince Roger are omnivorous and will happily try to take a bite out of their rider if given the opportunity.
Peachblossom in Protector Of The Small, though Keladry eventually wins him over. He remains temperamental, though, and she's pretty much the only person he allows near him.

Live-Action TV

On The Adventures of Brisco County Jr, Brisco's horse Comet is like this sometimes, when they've had a spat.

Music

"The Strawberry Roan" -- "I'll bet all my money the man ain't alive, that can stay with that bronc 'till he makes his high dive."

Real Life

Many donkeys can be like this.
It's also where the phrase "stubborn as a mule" comes from.
Anyone who rides horses on a regular basis has run into at least one of these.
Camels also have a tendency to be this.

Tabletop Games

In Dungeons and Dragons, there's an item known as the Obsidian Steed. If the rider is good-aligned, they must roll to control the beast or it goes to the Lower Planes and dumps them there.
Warhammer 40000: Juggernauts of Khorne
- Giant metal rhinos serve as beasts of battle. Being creatures of the god of rage, they are 'very hard to break in, which makes their riders all the more feared.
- Slaughterfiends are demonically-possessed machines that exist only to kill. Khornates make a point of trying to hitch a ride on ione, as such a feat vastly improves their status.

Video Games

Red Dead Redemption has a lot of unique and in some cases magical horses that must be "broken" before they can be ridden. And even a broken horse can still buck you off if you don't pay attention to the stamina meter.
The Elum in Abe's Oddysee is a grumbly cuss, but hopping on his back is the only way to progress through certain sections where the jumps are too broad for Abe alone.
Yoshi from the Super Mario Bros. series games will actually run around very fast and become very hard to catch should Mario or Luigi be thrown off his back after Yoshi is hit by an enemy.

Web Comics

The Adventures of Dr. McNinja: Yoshi the raptor won't let anyone but Gordito ride him. Unless Gordito is in danger.
In Freefall, Sam tries to ride Polly the emu to escape from an angry mob, but she refuses. He gets her to run by pulling off one of his facial tentacles and putting it on a stick
The Unicorn in Exiern allows the formerly male barbarian heroine Tiffany to ride but absolutely refuses to allow Princess Peonie to mount even when her life is in grave danger (probably because she's reputed to have been mounted more than a few times herself.) Lampshades are hung on both the implications and on the fact that Tiffany doesn't get the implications.

Western Animation

Looney Tunes: Yosemite Sam's camel and his dragon in the medieval episode.

Sam: "Whoa, dragon, WHOA!!"

- It's a Running Gag with him, having horses to do the same. Part of the gag is that he's too small to properly control the animals.
Goofy's mount in the Classic Disney Short "How to Ride a Horse."
There's a Pink Panther cartoon where he's trying to mount a horse who doesn't want to be ridden. Another has him as Paul Revere looking for a horse, and the only one available is on the British side.
Scrooge McDuck had a horse like this in his youth.