"Winter" is probably going to mean something different to you in Missouri than it does to me in Pennsylvania, but here's my scoop.
I just finished up my first year with chickens, and they spent the winter in a portable coop. I was lucky that we had such a mild winter this year. It gave me some time to think about what I would do in worse weather before my girls' survival depended on it.
"Portable" meant something different to me in winter than in other months. I needed a space that would be accessible to electricity to heat the chickens' water. This lead me to park the coop close to my garage. I didn't have a ton of space there, so I only moved the coop once a week (instead of daily). It was much harder to move the darn thing in winter because I had rigged a wind screen out of hay bales, concrete blocks, and leftover plywood. Even though I had chosen the spot to be partially protected from the wind, I still needed more protection from the wind. The chickens HATED it. Who doesn't hate freezing cold winter wind?
On snowy days, I did cover the run with a tarp. It was nice to remove the tarp, though, to maximize sunshine on clear days. My girls did not really mind the snow falling on them, but they didn't like to walk in it at all. Because my enclosed coop area is so small, I keep my food and water outside in the run. I needed it to be accessible all through the winter. I was fortunate this year to have the snow melt withing a week. If it had lasted longer, I probably would have tried clearing a new area for them, and moving the tractor there. The grass recovered nicely (even lush) where the tractor had been for a week. But I am thinking two weeks may have killed it off.
In very extreme weather, I rolled my coop into the garage for the night. My coop and run are in two separate pieces, and I had sized the coop to fit in the garage for this exact possibility. I'm glad this only happened one night last year because it was a pain, but I just didn't trust my own meager coop construction skills to keep the birds warm enough with negative wind chills.
Here are a couple highlights of my winter. Can you tell I've been thinking a lot about this? I'm not sure if I'll try for something more permanent next winter or not.
Freak October snow. It got me thinking hard about what winter would mean.
That freezing cold night when I just couldn't imagine leaving the girls outside:
A look at how the grass is handling a week of chicken life.