try using the code "SetOwnerShip" butt you must click on the unicorn, or the code will fail (i am not sure if i have written it right you can check it ut at "www.planetelderscrolls.com" it should be there). If you just want a horse you can join the dark brotherhood and do some work then you should get the best horse in the game called shadowmere that have good speed and if you lose it you may find it at fort fargut (i think i spelled it wrong) that is a littel above chyrdenhall (that one to) were it respawn, what i have read somewhere. and if you relly want the unicorn and whant to complete the quest you can get a unicornhorn from the testinghall the code is "coc testinghall" butt only take one or you will carry the rest of them for nothing and you cant use them. if you dont find the door just post again butt i think you will find it good luck .
actually - there is another way to take ownership. If you use a bow to kill the beasts (don't remember if the unicorn was in sight?), the unicorn has come over to me when I did see it and started following me around everywhere.