I assume you're referring to Cordyline and Yucca? Unless you have another palm tree with fan like leaves?
Nothing to be done right now - wait till spring and see how they are. If the Cordyline has a soggy or rotten trunk, you should cut down to where its healthy, or where new growth is occurring (which may even be at the base), but don't do this before end of May at the earliest.
It's a wait and see with the Yucca as well - you haven't said which variety you have, but there's not much you can do to reverse any damage which has occurred.