My chickens have been out all winter no issues. They do stay in the coop when it is snowing and just look outside but once it stops they are right out there! My run is covered and I have a heavy duty tarp on two sides and Plexiglass on another. They have a nice sand floor in the run and lots of shavings in the coop. I keep their food and water outdoors in the run and every morning they are happy to exit the coop for their breakfast and daily greens. I do put food in water in the coop when it is storming out but still keep the door wide open. You can see pics on my website of their coop
Love the site! Good luck with the cochins! My guys go out in the winter under a covered run.