A skeleton horse at night (Via Screenshot)
Skeleton horses don't spawn alone; instead, a skeleton horseman consisting of a skeleton riding a skeleton horse spawns. These hostile mobs only spawn from a “skeleton trap horse”, these are spawned due to a fraction of lightning generated naturally by a thunderstorm. A skeleton trap horse will never spawn if the lightning was caused by a trident or a lightning rod. When naturally spawned the skeleton trap horse will despawn after 15 minutes if not triggered.
To trigger the trap horse a player must come within 10 blocks of it, causing a lightning strike. The lightning strike will not damage any entities or start any fires but will instead hit the trap horse, causing it to transform into a skeleton horseman. Three additional horsemen will spawn around it. All the skeleton horsemen are spawned with an enchanted helmet along with an enchanted bow as well. In the Bedrock Edition, all the horsemen will be immune to any damage for 3 seconds after spawning.
Skeleton horses spawn in a river during a thunderstorm (Via Screenshots)
The skeleton horse along with its rider moves fast. They behave like regular skeletons, strafing and backing up when approached by the player. Skeleton horses can regenerate their health like regular horses and can be tamed by players, but they cannot be bred or fed.
You can tame a skeleton horse after you kill the skeleton that is riding it, after which you can tame them like regular horses by trying to sit on them repeatedly until it gets tamed.
When the skeleton horse is tamed you will see some particle effects in the shape of red hearts appear around it. To ride them you need a saddle. Once tamed, you can simply interact with the horse and open its inventory to place a saddle on its back. Once tamed and equipped with a saddle, players can now mount the skeleton horse and ride them around.
Like with normal horses, you can use as well as interact with items while riding the skeleton horse. A cool feature is that they will not kick you off if in water 2 blocks deep, and you can ride them underwater without the skeleton horse drowning, but the same can't be said for the player. When underwater, the skeleton retains its running speed and jump height from being on dry land.
A tamed skeleton horse equipped with a saddle (Via Screenshot)
Upon its death, the skeleton horse will drop between 0-2 bones, but this number can be increased by using an enchanted weapon with looting levels for a maximum of 5 bones. They also drop between 1-3 experience points and if they were equipped with a saddle, the saddle will drop as well (Java Edition only). Killing the babies is pointless as no items or experience is gained.
Skeleton horses are one of the fastest mobs for transportation in the game, but they cannot fit through tight spaces (single block openings). They can jump up to 5 blocks high, enough to climb hills and jump over fences. Since they don't drown underwater you can take them to any depth for riding along the ocean floor or river bed.
Skeleton horses were added to the game in v.1.6.1 along with normal horses. At that point in time, they could not spawn naturally but had to be spawned in with commands. This was fixed in v.1.19 when “skeleton traps” were added to the game, and now there was a chance for them to spawn if a lightning strike occurred (depending on the difficulty set). Minor updates introduced item drops and a reduction in spawning rates. They received new and more polished models in v.1.13, and by v1.14, they could be leashed with leads.
Skeleton horses are just better versions of their living counterparts. They are quick and quite agile, so scaling hills and obstacles are easy tasks for them. Getting a skeleton horse can be challenging as identifying when one has spawned can prove to be quite difficult, as you cannot go ahead and investigate every lightning strike you hear in a thunderstorm. If you manage to tame one, you will most definitely find it quite useful for transportation.
When a lightning strike occurs in a thunderstorm that doesn't damage the environment or hit any entities, there may be a chance that a skeleton trap horse has spawned.
When they spawn along with a skeleton horseman they are hostile mobs, but if you manage to kill the skeleton riding it they will become passive and you will be able to tame them.
If you are looking for them try to look in places where normal horses won't spawn, such as the middle of the ocean.