It’s not so much that they’re ’‘immune’’ to anything, rather than they don’t register anything as a threat, and perceive no signals to do something about any given threat that we humans do. (besides eating)
But they’re only ’‘not immune’’ because they can still be damaged.
Zombies could survive in -30 weather, maybe even more. However, their movement, already impeded by their physical disposition, would be greatly reduced. They would stiffen up due to the cold, and probably eventually fall, and no longer be able to get up. They would eventually freeze, but would not die. Extreme cold greatly slows the decomposition process, and sometimes even halts it. They would just lay there until Spring came, snow melted and then they would resume their activity as soon as they’re able to move. It is my belief that a zombie doesn’t die of ’‘starvation’’, but rather of decomposition (or at least until the small part of their brain which animates them rots away, as with nourishment it doesn’t regenerate) or destruction.
If it was in the North Pole or some other place that always has snow, I’m not entirely sure how indefinitely they would stay frozen, but probably a damn long time.
Sprinting zombies though, might be able to avoid being frozen, as they are much faster and active. But this is usually when they’re hunting. If there’s no one around for miles, the same fate as the classic zombie would probably befall it.
If you haven’t already seen it, I’d suggest watching Dead Snow. About zombies in the snows of Norway. Granted, it doesn’t explore much the whole technical side of zombies and weather, but it’s interesting nonetheless.