I'd be real careful with the "covered with tarps" thing, depending on what exactly you mean. First, as it is on natural ground, you need to leave a SUBSTANTIAL area open for the release of humidity - I would say, ballpark, maybe half of one long wall. Not just holes. Second, as a somewhat tall narrow structure, it is going to be vulnerable to blowing over if tarped, unless you have some serious earth-anchors on it anyhow. And finally, tarps are apt to shred themselves or just rip free of their moorings and leave, and if this happens during the middle of the night, you are likely to have dead or dying chickens by the time you discover it.
I would suggest using plywood (or whatever other solid material) to wall off a more houselike area that is protected from *any* direction of wind, leaving some ventilation (esp. high up) but with flaps or whatever to close the vents off as weather dictates. This plywood wall could be removeable for summer use -- your setup does look very climate-appropriate for the hot part of the year!
If you have any extra wire laying around, or pavers, or anything like that, it would also be worth doing some sort of apron type dealie to discourage predators from digging in under the edge and having chicken dinner. Predators get especially hungry in the winter, and the ground isn't always frozen.
One last thing, how much snowfall is it possible for your location to get? Not average snow, but I mean, what's the most you can ever remember it snowing? If it's more than 6" or so, I would suggest beefing up the roof/run supports and adding some diagonal bracing. If it is never anything like that much, you are prolly ok.
Good luck, have fun,
Pat