It should be OK if the cold spell is brief and doesn't dip to below -10. Any leaves which are frost damaged and become unsightly can be removed, they'll soon be replaced in Spring. (The frost damage won't be evident immediately.) If the cold spell is expected to be prolonged, this article may help you now: Protecting Palm Trees in Winter (hardy-palms.co.uk)
That's actually a REALLY good article that I didn't find in my search. "Spike" has been neglected for 10 years, so I think he's probably tough, but I'll chuck a fleece over him to be safe, as he had a recent stressful removal experience. Thank you, as always
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h4: hardy through most of the UK (-10 to -5)
https://www.rhs.org.uk/plants/3695/chamaerops-humilis/details
Billericay - Essex
Knowledge is knowing that a tomato is a fruit.
Wisdom is not putting it in a fruit salad.