This summer I've been making neck coolers. The most annoying part of the whole process was turning the loop the right side out. I fiddled with them for what seemed like forever. I tried making my own loop turner out of a chopstick and a wire, but it didn't really work. So I presented the problem to my husband. He likes to solve problems. Within minutes, he came up with this idea.
He grabbed a 5/8ths inch dowel rod from the garage (I'm sure a half inch dowel rod would work just fine too). He slipped the neck cooler tube onto the dowel (in picture above). Then he used a tack to attach the fabric to the top of the dowel rod. He later discovered that a push pin (with it's slightly longer pin) worked a bit better. He also determined that pushing it through the fabric where the seam is (and consequently more layers of fabric) help to keep it attached to the dowel.
Once it's attached comes the fiddly part. Carefully pull the surrounding fabric up off the dowel to get it started.
Keep pulling a little at a time up off the dowel rod. He held the dowel between his feet while he did this.
When you see the right side of the fabric come out the bottom of your tube (in other words: when you're half way), you can pull the whole tube right side out. This process allowed us to turn the tubes right side out in a fraction of the time of doing it by hand (and it got my hubby to help out with a craft--miracles have been worked here I tell ya!).