My pop door faces north and the maintenance doors (one whole wall of the coop opens up) face east. I have windows on the east, south, and west sides. My doors are positioned as such simply due to the fact that that is where we had room to put them. During the winter, I wrap the north and west sides of the run in tarp and stack straw bales along the south and west sides of the coop (my coop is elevated 2ft up) as well as using straw bales to hold down the tarps. Seems to keep the girls happy. With solid privacy fencing you probably won't get strong enough winds to make a huge difference in which way is best for the coop door. If you are concerned, you could always wrap one or two sides of your run to provide a wind block for your chickens. You could also use straw bales to make a wind block just in front of the door, although it looks like your run is a little small for that. Looking at your coop, I would probably face the door south if possible to take advantage of the sun's warmth in the winter. In the summer you could rotate it so that the door faces north if you get very warm.
