I believe that the undead mobs in vanilla Minecraft should be able to spawn alongside the Barrow-Wight mob in the Barrow-Downs within Middle-Earth. With certain exceptions, the undead mobs that should spawn are as follows:
Zombies, Baby Zombies, Husks, Baby Husks, Zombie Horses, Skeletons, Strays, and Skeleton Horse Traps: They are all undead mobs and including them within the Barrow-Downs would give diversity to the Barrow-Wights. While these undead mobs aren’t Barrow-Wights, they do fit the Barrow-Downs and they don’t need to be called Barrow-Wights to be among those that the Witch-King cursed to haunt that land.