From what I can tell, P zero's are summer performance tires. If you wait until the roads are plowed and ice free, no problem driving with them. Summer performance tires suck big time even if you have AWD in the winter.
You're close. Let me explain: I wouldn't choose them for heavy duty snow rallying (I've actually done that, successfully).
In my lifestyle, I only go out in cold, light snow conditions; for a variety of reasons. I'm old, and wouldn't want some idiot hitting me and forcing me to endure standing around waiting for a tow or worse in the Winter. Two, cold itself is a factor and they are good for that. Three, they are run-flats, which I like. And lastly, I don't have to drive at all, since I'm retired, so if it's questionable conditions, I just turn up the heat and stay home!