Yes, as hard as it is to do so.
I have the same thing on mine, and I was really consistant about covering them.
Last year mine froze horribly, but Dave the Garden Guy had said not to trim them until March.. (The parts that are already dead help protect the plant from any further damage.)
I made it until about half way through Feb ;)
They came back stronger and better than ever!
Have faith, he will be ok in the long run.. before you know it we will be trying to keep them alive in the Heat lol