I have woven a new style of scarf/cowl that I saw recently other places on the internet. I cobbled together some hints and tips and was very successful weaving it. You leave some unwoven warp at the beginning of the warp, weave for the desired length minus the width, then unwind and untie the beginning and weave the fringe in as the weft at the end. I hemstitched up the side as I wove in the fringe and across the end when I was finished. I can wrap it twice around my neck and I like to wear it with the fringe off the 
shoulder.
In my opinion, a nice aran or light bulky weight variegated yarn makes a lovely cowl. I think a plain solid, heather or semisolid would look great too. I don’t care for the plaid you get if you use a striped warp. The rigid heddle loom is the ideal tool for this. I think it would be trickier on a table or floor loom. I call it a V-cowl and I plan on teaching a class on how to make it at the Weavers Guild after the first of the year. Check back in a couple weeks to see the detail.