Lightning spawns Skeleton Horse when doMobSpawning is false. More detailed description from MC-93678:

Skeleton horses with SkeletonTrap:1 spawned naturally in my world which has had gamerule doMobSpawning false since its creation. ( Gametime is about 2970313, difficulty was HARD )

These SkeletonTrap horses successfully spawn skeletons.

Can confirm this by manually spawning horse:

/summon EntityHorse ~ ~ ~ {SkeletonTrap:1}

It will instantly trigger.

Confirmed they are aggressive, and the skeletons will despawn from the horses if difficulty is changed to Peaceful.

Trapped horses trigger when in Peaceful difficulty, however no skeletons are on the horses.

Additional useful information:
Lightning does not affect the SkeletonTrap horses. The mechanic is 100% proximity based.
Reproduce: Spawn a SkeletonTrap horse away from you, within vision, run this command with that being the closest horse to you:

/execute @e(type=EntityHorse,c=1) ~ ~ ~ /summon LightningBolt
except use brackets [ ] instead of parenthesese ( )

You will see this horse not expand out with or without skeletons. Instead, if it is not raining or in water, you will see it burn.
Further confirm by approaching the horse and seeing it trigger and expand.

The effect is not lightning; it only looks like lightning.