Alianora Munro has created a pattern for a "Fourteenth-Century Style Knitted Hood with Lirripipe." The pattern, with photo, is available on the Belfry Knits blog.
I designed and knit this hood more as an exercise in creativity and pattern-drafting than as a highly authentic garment based on surviving evidence. I had lucked into the yarn, a very nice shaela Shetland wool, and wanted to do something special with it. People definitely were knitting in the fourteenth century, but evidence that they were knitting hoods is hard to come by. I am told that in her book A History of Knitting before Mass Production, Irena Turnau presents some evidence for knitted hoods in eastern Europe during the Middle Ages, but I have been unable to get my hands on the volume to see what that evidence is, and since furthermore the quality of the English translation of her original Polish text is not said to be particularly good, it might be hard to tell if her "hoods" are the same kind of thing as western European ones.