Is this coat warm enough for real winter?

It is midweight with 100% synthetic fill and a hood, so it suits cold days and layering. For sub-freezing or windy conditions, plan to wear a sweater underneath.

Does it really pack down?

Yes, Calvin Klein lists it as packable. It compresses into a bag or suitcase, which makes it a good travel coat, though it will not shrink as small as a down jacket.