Your eyelashes keep freezing to your hairy hat.
Your plug-in cord acts like a frozen snake.
You wonder if plastic-y dog food bags will split open if you try to carry them inside. Or would it be better just to leave it in the car for now?
You can blow frozen bubbles.
How long you spend outside depends on how fast your fingers freeze. In gloves.
You warm up your car for half an hour, but still have to drive 20mph until your tires get unsquare.
Your male dog pees standing on two legs. Both your dogs would levitate if they could. One of my dogs did attempt pooping while balancing on his two front legs!
It takes 15 minutes to put on enough gear to walk the dogs for 10 minutes.
Fifty percent of the cars in the parking lot are running.
It's clear at your house, but once to get to town you can't see doodly for the ice fog.
You have special temperature sensors set up to monitor your water pipes/tanks.
The first question people ask each other is, "What's the temperature?"
You leave your car running, with the dogs inside, not because they'd get cold, but because if you don't, the windows will be entirely frosted over with dog breath when you get back.
The bunny boots come out!
If you lock yourself out of your house, it's a real emergency!
You have a cooler in the car to carry home groceries that you don't want to get frozen.
You wear so much gear you can barely bend from the middle and look like the Michelin Tire Man, just like everyone else. (Arctic Nightmare for men: out on the trail with 7 inches of clothing and 6 inches of peeing equipment!)
You are really, really, really glad you moved into that house with the indoor plumbing!
At night you know another car is headed toward you on the road because you can see their headlights towering straight up in the air. (Nope, it's not aliens!)
Feel free to add more...