I retrived Arvak's skull but the objective to do so does not complete and the quest does not progress
I've found Arvak's skull in the Soul Cairn and picked it up, but the objective "Retrieve Arvak's skull" remains active and the soul who is supposed to give me the spell to summon him does not appear. How can I complete this quest?
You need to input the console command
setobjectivecompleted DLC01SoulCairnHorseQuest2 100 1to get the stage to clear. After that's done, the soul will appear and the quest will complete properly.