I've experienced the same thing with my Xanadu (crazy Texas weather, right?), and I'm assuming the cone-like center of the plant is still firm, not mushy. If the "stems" are still there without the "leaf" part (the long stem is actually a petiole) you can either cut them off where they emerge from the cone-like center, or wait for them to totally dry up, at which point they'll just fall off. I prefer the first choice - makes them look better faster in my opinion. A little patience is needed to allow for the plant to send out a bunch of new growth to replace what was lost. But with time, you should have a decent looking plant - hopefully by the end of summer. :-)
Thanks Nifty. I did cut all the stems off and I have noticed the new leafs coming out. It rarely freezes where I live in Houston but it was that one night I wasn't prepared for. Unfortunately, it was a lovely large plant so it will take it a while to return. Like you mentioned, crazy weather this year!