When summoning a zombie or skeleton horse they do not despawn even when given tags to make them do so.
/summon minecraft:zombie_horse ~ ~ ~ {PersistenceRequired:false}
/summon minecraft:zombie_horse ~ ~ ~ {PersistenceRequired:true}
Fly far away, both will still be there regardless of tag
For the Zombie Horse MC-48071
As for Skeleton Horse I believe this is intentional. They are treated as passive horses.