Baby, it's cold outside!

The prototype was redone many times.

Warm and woolen.

Okay, as promised, here are my attempts at making infinity scarves. They are basically lined tubes of fabric. I've used some soft jersey material, silk/cotton blends, cotton rayon blends and rayon/wool blends.
As I mentioned in a previous post, I had a bit of a brain freeze trying to put them together, but once I realized you have to sew the long ends together, with rights sides together, first -- then I got cracking on at a blinding pace. (I can hear the snickering out there...)
The measurements are random and varied as I worked out how each fabric would drape. At some points, I used my sewing machine's walking foot because some fabrics weren't meant to butt up to each other like that. When they do, they fight a bit for supremacy. The walking foot plays the peace maker and makes each of them get along until they are sewn together. I also found that if you use a wide zigzag, all the fabrics not only line up properly, but they retain their stretch when it comes time to wear the scarves.
Basically, you cut a strip of fabric about 33 cm (13 inches) wide.  You'll be using the fabric's whole width, selvage to selvage, so you'll end up with a strip of fabric that is 33 cm wide (13 inches) by 140 cm (45 inches) or 150cm (60 inches).
Cut two of these strips in contrasting colours, and decide which will be the main colour. Pin right sides together, and sew the long edges together, using a wide zigzag stitch. Go slowly, so you don't break your needle on the pins. My seam allowance is .5cm (1/4 inch)
Turn the scarf right side out.
Pin the main colour ends -- right sides together -- matching the side seams as closely as you can. Then, on either side of that seam, pin about 7 cm (3 inches) of the lining fabric right sides together. Sew together in a continuous seam, taking care not to catch the rest of the lining in the seam (happened to me twice, and I said some bad words). You'll have joined the main colour together and have just a bit of hand sewing to close up the lining seam.
Eh, voila! A scarf that is both a cowl and a hood. They are very comfortable and warm.

This is one I made for me. It has Hawaiian shirt material on one side and rayon jersey knit on the other. Special thanks to Phoebe the foam head for her help in modeling the finished results.

If you want to wear it as a cowl, you put it over your head so it is a giant necklace, then you twist it once and pull it over your head. If you want to make it a hood, just pull the twist up over your head.   
I did most of mine with a jersey/rayon blend that I found in the remnant bin for $3. The work best with soft fabric that drapes nicely. This stuff isn't easy to sew, but I like the results.
I did a bunch of these for my daughter, Miss B. They will be winging their way to her tomorrow.