A skeleton horse can be tamed by killing the skeleton that is riding the horse. Then, the player will be able to tame it. A saddle is required, too.
A “skeleton trap” horse is a skeleton horse spawned from a fraction of lightning strikes during a thunderstorm (0.75–1.5% chance on Easy, 1.5–4% on Normal, and 2.25–6.75% on Hard, depending on regional difficulty).
Currently zombie/skeleton horses have no use, cannot be tamed, and can only be spawned through the use of in game commands. To bring them up to par with regular horses they need to be tameable somehow and capable of wearing saddles and horse armor. …
The rarest regular spawning horse is easily the skeleton horse…
Skeleton horses should behave like skeletons (Burn in the sun & despawn quicker in the day) … The only way to find/ capture a skeleton horse is if a living one gets struck by lightning.
A lightning strike affects certain mobs differently: Lightning may randomly spawn a “Skeleton Trap” Horse with a chance of 0.75–1.5% chance on Easy, 1.5–4% on Normal, and 2.8125–6.75% on Hard, depending on the regional difficulty. … A pig struck by lightning turns into a zombified piglin. A creeper becomes charged.
Zombie horses, like most mobs, can ride in minecarts and boats. Unlike other passive mobs, zombie horses slowly regenerate health.
How to Enter the Command
In Minecraft, you can not feed a skeleton horse! Since a skeleton horse is undead, the Instant Damage effect will restore health points to the skeleton horse. Try throwing a splash potion or lingering potion of Harming at the skeleton horse or shoot an arrow of Harming at the skeleton horse to restore its health.
Skeleton horses are rare mobs that are a variation of skeletons. They can spawn if a horse is struck by lightning. They despawn very quickly though. Unlike regular horses, they will not kick the player off if they go more than 2 blocks underwater but will sink instead.
A skeleton horse that spawned from a skeleton horse spawn egg cannot be ridden on, open its inventory, put a saddle on it, be tamed, feed it. An undead horse that spawned from an undead horse spawn egg cannot be ridden on, open its inventory, put a saddle on it, be tamed, feed it.
You can summon a horse that is already tamed, wearing a saddle, and ready to ride whenever you want using a cheat (game command) in Minecraft. This is done using the /summon command.