Dont think that cutting the top off a genuine palm will do much good as they grow out of the top. I'd take off the dead bits and wait and see, may well send out start sending out some new growth when the weather warms up - like now!!
We have been persuaded to buy all manner of palms over the last few years on the back of our 'definate' climate change. This winter has sorted out a lot of the less hardy stuff. Not long ago it was recommended that palms be wrapped up for winter with sacking and not to be undressed 'till spring.
However if its a cordyline and the top has rotted, then cut it back and it may well shoot out from lower down