Sorry, I get so hung up on details.
To say you are a bit cold in Spanish the only correct way is:
Tengo un poco de frío.
It is a bit difficult to see why because we use different verbs in Spanish and English ( Tengo ... vs I am...) When you say a bit of something (using a noun) in general you need "de", but if what to say "a bit something" with an adjective, you don't need "de".
See two contrasting examples:
I am a bit cold (Literally I have a bit of cold) -here cold (frío) is a noun, not an adjective.
Esta bebida está un poco fría.
This drink is a bit cold. - here cold is an adjective.
I hope it clarifies it.
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