Your hug is a warm blanket on a cold day is it a metaphor?

Yes it is a metaphor. Which is a figure of speech in which a word or phrase is applied to an object or action to which it is not literally applicable A metaphor is a figure of speech that, for rhetorical effect, directly refers to one thing by mentioning another. It may provide clarity or identify hidden similarities between two ideas. Antithesis, hyperbole, metonymy and simile are all types of metaphor

Yes. It is comparing something to something unrelated without using 'like'or 'as.'