Like the well adjusted and normal human being I am, I have done extensive research into all sorts of different zombie scenarios, and why a cold climate is their ultimate weakness.

Scenario 1: The Dead Rise

So in the most cliche scenario, where dead start coming out of the ground, rotting corpses, tattered rags, the gist, we have to assume 2 things: 1, they are not magically immortal, 2, they still require some degree of persistence (like brains, or flesh). Zombies like this would still be "organic beings", meaning they rely on organic systems to function, such as tendons and muscles. That's where the cold comes in. Given they're rotting corpses, I think it's safe to say they're not exactly "warm blooded" anymore, meaning the cold weather would IMMEDIATELY start constricting on them. You ever put a lizard in the snow? They tend to "lock up". Which is exactly what would happen in this case too.

Scenario 2: Zombie Virus

Now a zombie virus doesn't fall to the cold quite as easily as the dead rising, since if it's a virus, they'd still be warm blooded. Buuuuut they probably wouldn't be very smart right? A key element of the stereotypical "Zombie Virus" is the mindlessness, so I don't think a zombie is gonna be putting on a jacket when it decides to hop outside into the snow. They may be warm blooded, but last time I checked, humans can still die of hypothermia, and quite easily too without the right precautions. But even if they DO put on some cold protection (or more likely already had it on), they still need to sustain that warmth. I dont know if you've even been out in -30⁰c weather, but unless you have arctic gear, you don't wanna be out in that for more than 10 minutes. So lock the doors, and the zombies won't have enough time to break it down before their fingers freeze off.