You can compost it. I would cut it up some first though. I have put ornamental grasses in mine but the thicker leaves take longer.

Carey

Since this is a plant material, and since this does not root from the leaves (that will be composted) you can compost them. If your composter is not working well that may be an indication that your C:N ratio is off or that the material is too wet or too dry. Even now, up here where the average temperature is running around 20 degrees, my compost is out there being digested so if all conditions are about right for the bacteria that digest what you put in then simply that it is winter does not mean you cannot compost.