Let it be. Unless a twig turns to smelly, rotting mush, do not prune to remove it. You may still have further bouts with frosts and cold, so any pruning could lead to re-leafing and further harm.

Prune it in late March (after no further danger of frost) when you see a strong regrowth of foliage and it becomes very apparent where the dead twigs are.

On a side note, are you SURE it's a royal poinciana (Delonix regia)? They are more of a zone 10 plant. Do you possibly have a dwarf poinciana (Caesalpinia pulcherrima), that makes much more sense for coastal SE Texas?

Thanks for the response!! No, I'm not sure if it's a dwarf or a royal. I bought the plant in the valley region of deep south texas 2 years ago. Like I said it is at least 10 feet tall at this point. Do you know when it may bloom? It did not bloom last spring/summer. We live on the coast of SE texas just west of Galveston so I think we're in zone 9? Thanks!