Nothing yet, unless the trunks are rotting, pouring out orange stuff anywhere, in which case you'll have to cut back past that point. Any cutting best left till spring, so if the trunks aren't rotting or oozing, leave them alone, wait for new growth to appear either up the trunks or from the ground, then cut back to that point. If new growth appears...

I have a canary island date palm, as well as a cordyline, both appearing 'dead' at the moment, but they did so last year too.

I am doing as Bamboo says. My cordyline started to sprout again last year , and my palm had new fronds from the centre, but I had to wait until the summer to see any of this... nearly wrote them both off.

It will be a waiting game this year too. fingers crossed they pull through this year, and I get the 'winter protection' balance right next year!!!

Thanks to you Heidib I will be keeping my canary island date palm as I thought I had lost mine too for the same reasons you stated above.I will hang in there in the hope mine too will pull through.