Well, there is cold weather camping and there is really cold weather camping.
In cold weather camping you build a fire and sit around it, trying to stay out of the smoke. In really cold weather camping, you fight for being in the smoke because it’s the warmest part of the fire.
In cold weather camping, you have plenty of water. In really cold weather camping, you spend a hell of a lot of time and fuel trying to keep your water from freezing.
In cold weather camping, you don’t mind being outside the tent. In really cold weather camping, you either want to be out hiking or inside your sleeping bag. Sitting around camp in really cold weather is no fun.
In cold weather camping, small problems are small problems. In really cold weather camping, small problems can become really big problems.
For me, 10-20 degrees is cold. 25 below zero is really cold.
If you use a tent, use a 4 season tent. Use a good sleeping bag and sleeping pad. Have plenty of fuel. Be careful about using a lantern in a tent. It’s warm, but it can be deadly. I use them, but only with the windows open a bit for ventilation, and I turn them off when I go to sleep. Getting out of the tent to piss isn’t too bad if you do to things: have some slippers or shoes nearby, and have a flashlight ready. Get those two and even in really cold weather it’s not a problem. And a good sleeping bag is one rated for really cold weather. Rent or borrow one if you don’t have one. A -25F bag is a nice thing to have and can make the difference between a good time and misery.
Don’t do stupid shit. A minor injury can be a big pain in the ass in cold weather. Cars get stuck in snow or just don’t start. Don’t absolutely depend on them, and take care to make sure they will work if you need them.
Dry clothing. Layers. Caps and head covers.
And have fun. It’s a blast.
One last thing. The worst weather always seems to include high winds,which makes a hell of a noise in a tent. Take earplugs if that might bother you.