On your way to the imprisoned vampire in Soul Cairn, you will be stopped by one of the souls. The man will ask you to find the skull of his horse.
In order to find it, head to the castle where Valerica is waiting for you and keep going east afterwards. At some point, you should notice some ruins with a couple ghosts around it on the right
When you get closer, the area will turn purple and the souls will change into deadly skeletons. Quickly defeat all the enemies and pick up the nearby skull.
In order to finish the mission, you need to take it to the soul marked on your map.
In return you will receive the Summon Avrak spell (found in Conjuration), using which you can summon an undead horse.
It will come in handy to complete all other missions in Soul Cairn.