Answer: Don't give up on your palm just yet. As long as the growth bud in the top center of your palm is alive, your palm will develop new growth. You can prune the brown fronds off, or just leave them alone until new fronds emerge. I don't think your palm has suffered permanent damage because of the frost, so I wouldn't dig and replace it - at least not now. Give your palm a chance and I think it will recover.
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