How do Zombie and Skeleton Horses spawn?

They do not spawn naturally and aren't meant to. But you can spawn them via commands.

/summon EntityHorse ~ ~ ~ {Type:[insert number],Tame:1}

If Tame:1, it is a tame horse. Tame:0, its not.

Type:3 spawns a Zombie Horse, and Type:4 spawns a Skeleton Horse.

You cannot find Zombie or Skeleton horses in the wild.

They can only be spawned with the following commands:

Tamed Zombie Horse: /summon EntityHorse ~ ~ ~ {Type:3,Tame:1}
Untamed Zombie Horse: /summon EntityHorse ~ ~ ~ {Type:3}
Tamed Skeleton Horse: /summon EntityHorse ~ ~ ~ {Type:4,Tame:1}
Untamed Skeleton Horse: /summon EntityHorse ~ ~ ~ {Type:4}

In 1.9, Horses can now be dangerous. If a horse has the tag SkeletonTrap and you come within 10 blocks of it, it turns into a skeletal horse with a skeleton riding it. The skeleton can't despawn and has an enchanted bow and enchanted iron helmet. If that were not bad enough, three others also spawn when you trigger the spawn.(FYI the skeletal horse is tamed and can be ridden with a saddle)