I think "wrap up warm" is fine, actually. There's no rule that sez that an adverb has to end with -ly, or that one that does end with -ly can't evolve into one that doesn't. I'm only guessing, but I suspect that the injunction "wrap up warm" is commoner than "wrap up warmly." In that context, "warm" is still an adverb. If enough people use a construction for long enough, it becomes standard English whether we like it or not. Another battle lost, I fear!

And I'd far sooner hear a weather presenter advising me to wrap up warm than telling me that "five degrees will feel more like minus one in that breeze" which is just gibberish! How many people have an accurate and objective understanding of what "five degrees" or "minus one" feels like? Is that with your coat on or off? When you're wet or dry? Felt on your hands, your feet or your face? Whether you're fat or thin? With your thermal knickers on or off?