I can't bring the image up, but judging by your description I'm going to guess that you've found the mobile home of a bagworm. Not a cocoon, at all, though the caterpillars will lay her eggs in them before so that they can overwinter safely.

It's a bagworm. If you see a lot of them, and I mean A LOT, you might consider hand picking some to reduce the overall population. They can be very destructive to some plants.

Jmcat, the 'bag' of this insect is made of silk, and very strong stuff, too! Try tearing one apart and you'll see what I mean.

Male bagworms use those bags to pupate in, emerging as sorry looking raggedy moths. The females never turn into much of anything, don't even look like a caterpillar! After mating, the females will lay her eggs and eventually drop to the ground to die.