Your link didn't work but I found the hat you are referring to. Those look like they have been wet felted as opposed to needle felted. But you can make a "snake" by rubbing the fiber between your hands and then needle felt it down to shape. I personally think it would be easier to wet felt it though.
I have read about wet felting, but I didn't read anything about how to make the spiral even in the wet felting. I was thinking about inserting a small wire.....that was part of the very first needle-felting tutorial I viewed; she was making a small mushroom and the stem was wrapped around a wire so it could be bent into whatever shape you wanted.
when you do it with wet felting you make a snake like you do with play clay. You wet most of the wool and leave one end dry for attaching to the hat. Roll it like the snake until it is firm. Then while it is wet you wrap it around something like a pencil ( or something bigger if you like) and let it dry that way. Do some sample snakes around different things to see how much curl you get. They are fun to do.
Thanks, Shepherdess! I actually did wet/soap the tip that I have on the hat, squeezed it all out (rinsed it, too) like with wet felting and tried to form the spiral. A spiral is a different shape than a pig's tail curly-q. I saw someplace that wrapped it around a pipe cleaner but, again....that gives me a curly-q and not a spiral. I guess I could do as you say and then pin it down on my foam block into my spiral and then attach it when it's dry.