I saw something similar at Ikea a while ago and decided to make one to hang my scarves.
I hope the how-to will be useful :)
(sorry in advance for my crappy english)
First of all, we need to get rid of the triangular shape of the hanger. You will need some strength to do this and I recomend you use pliers on each ends of the hanger.
Measure you hanger. Divide the lenght by 3. The result will be the diameter of your circles.
Use a compass to draw on the cardboard the circles. Draw a smaller circle on the inside of the circle you just drew (the distance between the circles should be a little less than 1"/2cm).
You really need to use a thick, strong cardboard, or else the result will not be that good.
Cut one of the circles/loops with a box cutter and use as a templet to cut all the loops. I used 9 but you can use many as you want, as long as the total number of loops is a multiple of 3.
Cut 1"/1,5cm stripes from your fabric and cover the loops.
If you're using different fabric colors, chose now the color scheme of your hanger.
Use the thread (I used crochet thread) to join the loops. Just wrap several times both loops with the thread.
This picture shows where you should join the loops.
Cover the hanger with fabric as you did with the cardboard loops.
Attach the loops to the hanger and you're done!