Did not think to ask when I purchased my shiny new surface - how to protect from viruses. I have spare N360 licences but it would not download....
Welcome to the Norton Community Forums.
I am sorry to say that I do not know the answer to your question. While Norton 360 works with the full desktop version of Windows 8, despite what Microsoft implies, as far as I am aware the versions that run on the Surface are different and not supported. Norton Mobile Security provides protection for Android and iOS tablets but not for Window tablets, and even then the licence for the Normal Norton 360 does not cover tablets.
I assume there is some sort of App store for Windows Surface/Windows RT and you could look there for suitable apps or go back to whoever sold it to you and see what they recommend.