I read the part where you said you don't want to make one, but hear me out. It takes 10 minutes.
Buy a wool blanket from military surplus store, or a fleece blanket. Or get a coupon for a fabric store and get some fleece.
Half Circle: Either purchase fabric that is twice as long as it is wide, or do what you can with your blanket. Fold it to make it as square as you can. Draw a quarter circle using chalk or something on a string, with a radius as long as the shortest dimension of the fabric allows. Then at the corner, draw a quarter circle with a radius of 6 inches. Cut where you drew. You have a half circle cloak with a 19 inch neck opening. Pin it shut or if cutting fabric inspires you to keep the crazy craft spree going, cut two strips of fabric out of the excess fabric, and sew them in as ties. This kind of cloak won't stay closed in the front unless you're holding it that way. It's not exactly convenient in combat. But neither is a blanket pinned around your shoulders.
Poncho: Fold in quarters. Keep track of which corner is the center of the blanket. Draw a quarter circle for the neck opening (radius: 3 inches). Cut off the corner. Now you have a neck opening that is about 19" circumference in a poncho. Enjoy your poncho. Or make a slice up the front and use a pin to keep it shut and you have a poncho-style cloak. It should stay closed nicely and not terrible for having free hands. However the sides are open so there goes your heat out the sides when you raise your arms. But if you put a belt over it, and fidget until you can move your arms freely, you're set.
How quickly do you need this cloak?
Edited - For the Half Circle I corrected the radius of the quarter circle to 6 inches. You're only folding the fabric in half, ending up with a half circle, and then that has to go all the way around your neck. If you do the poncho, the radius is only 3 inches because you're going through four layers of fabric and actually creating a full circle with your one cut.