Soul Cairn Horse Quest

Walkthrough
Along the north-east path from the portal, just before crossing the breach in the great wall, a soul may tell the Dragonborn about missing his horse Arvak, not being able to find it anywhere in the Soul Cairn.

Find Arvak's skull in the Soul Cairn
Arvak's Skull can be found on a pedestal just east of the Boneyard entrance, down the hill.

Retrieve Arvak's skull
Pick it up.

Return Arvak's skull
Luckily Arvak's rider will have moved and be quite nearby. Give him the skull. The Dragonborn will henceforth be able to summon Arvak (a horse) at any time via Summon Arvak spell.

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