Ventilation - Read Pat's Ventilation Page. And note that Pat lives in Ontario so she knows cold winters.
https://www.backyardchickens.com/web/viewblog.php?id=1642-VENTILATION
Hot air rises. The way to get ventilation is to have ventilation slots high and low. That way the cooler air comes in from outside through the low vents and warmer humidity and ammonia filled air escapes through the high vents.
I'll expand a bit on what BuckeyeDave said. Chicken poo gives off ammonia, especially when it is wet. Ammonia can cause respiratory probelms in chickens. Ventilation gets rid of ammonia.
Chickens can handle cold quite well on its own, but if you add high humidity, they run into problems. I've read posts where chickens got frostbite at fairly warm temperatures and am very sure it was because of inadequate ventilation. Chickens and chicken poo both give off water vapor, which raises humidity. Cold air cannot hold much water vapor before the relative humidity gets pretty high.
Another thing to watch for is drafts. Getting ventilation without drafts can be tricky because of the wind. I'd suggest ventilation openings, covered with hardware cloth, with flaps high and low on different walls so you can close the ones in line with the wind.
Another thing you might consider. If you put a low vent opening on the southeat corner, a high opening on the southwest corner, and your roosts on the north side, you would get a cross-current with them out of the worst of the draft. Choose the corners that suits your location, but maybe you catch the concept.
Second: the Floor.
Sounds like you are planning on a fairly large coop so you will have to go inside for poop management. However, I don't know your poop management plan. Some people use the deep litter method (dlm) and clean out the coop every 6 to 12 months. Others use a poop board and clean the coop daily. Many are in between. This influences your choice of floor covering. If you clean daily, (I will not) use sand. If you want more on the dlm, use search on this site or google. As your chickens will probably spend a lot of time indoors in the winter, you probably want something that will absorb the moisture but that they can scratch and mix up. Sand would work. A lot of people use pine shavings, available at feed stores in bales that do not cost that much. Straw ends to mat and is hard to remove when you clean it out. Chopped straw would be better if you want to go with straw.
Chicken wire will keep chickens in. It will not keep most predators out. A coyote or raccoon will rip right through it. Hardwire cloth or 2" x 4" welded wire will stop them. I'm thinking that is why you would consider burying wire in your coop. An option, if it suits your set-up, is to put an apron around your coop. Put 18 to 24" wide hardwire cloth or welded wire horizontal around the outside of your coop and bury it about 2". This is usually the thickness of your sod. Some people put it right on top of the ground and let the grass grow through it and hold it down, but I'm a clutz and would get the weedeater of lawn mower into it. Attach it to the bottom of your coop or run it under the edge of your coop about 6". A predator will come up to the coop wall, start digging and run into the wire.
You could bury the wire in your coop floor. Sounds like you have access to dirt and sand. If you put a couple if inches of dirt on top of the wire, then put sand, you will know to stop cleaning when you get to the dirt. This will also raise the level of your floor where outside water will not come in and, if you mound it a little, water will drain better from your coop.
I'm an engineer, so by training and nature both I tend to overthink, overplan, and overanalyze. This tends to raise the blood pressure. And this stuff does not have to be this difficult. Chickens are very adaptable. As long as you provide for their basics, they will do well. And treat everything I've said as you do everything else on this site, as general guidelines. You have to also be adaptable and make things work for your specific situation.