Question
You had mentioned if a Pygmy Date Palm may have frostbite a person can try spraying the center with a copper fungicide.  So should all the dead palm branches then be cut off?    

Thanks

Answer
If the fronds are completely browned out,,then yes, sever them at the trunk, but if there is any color left, leave them be until they brown out completely, for they are still functioning at that stage,,,and the Palm needs all the help it can get when cold stressed.