All about the ancient tribes
You can summon a zombie horse whenever you want using a cheat (game command) in Minecraft. There are many options for summoning zombie horses. You can spawn one that is wild, tame or wearing a saddle. A zombie horse does not spawn naturally in the game so you have to use the /summon command to spawn one.
The zombie horse should spawn! You can put on a saddle, not horse armor. Be sure you typed this: /summon EntityHorse ~ ~ ~ {Type:3, Tame:1} (If you want a Skeleton horse type the same thing, just change the 3 to a 4.)
The game control to tame the skeleton horse depends on the version of Minecraft:
Zombie horses can now be tamed and leashed. The textures of zombie horses have now been changed.
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.
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 skeleton horse will be tamed, and ridable, if you hold a hay bale to it. However, I think this is only possible if it was spawned. Here is tutorial of how to tame and ride a horse, put saddle or armor on horse and get off it.
Steps to Tame and Ride a Horse
How to Tame a Cow in Minecraft
Breeding. Horses are breed-able by riding them and right-clicking on them with golden carrots or golden apples.
Baby zombie horses can be spawned, too. They do not burn during sunlight.