I have the same setup, but in northern Indiana. Instead of draining, I actually filled the pool completely full right to overflowing. I did this so I don't have to worry about pumping the water off the cover this winter, as I will be down south for several months. I put an empty gallon jug into the skimmer inlet, a 1-1/2" PVC pipe with male adapter and rubber ring inside the skimmer instead of a gizmo, plus filled the skimmer up with closed cell foam as well as another empty 1 quart bottle. This way there really isn't much water, relatively speaking, inside the skimmer and any that is and does freeze wont' be solid enough to cause any damage. In addition, the water in the skimmer is about 18" deep, so I don't think it will ever freeze at the bottom unless we have an extraordinarily cold winter.
I blew out all the lines, including the skimmer and main drain, and shut the valves to airlock them. I also poured antifreeze down into the skimmer pipe just to make sure, but this level is about a foot below the bottom of the skimmer, so it shouldn't freeze anyway. The returns were blown out with a shop vac very thoroughly, with a plug in the one, then plugged the other with the air bubbling out like crazy. Note, this is a great way to get wet! By leaving the shop vac on and alternating between both returns, I was comfortable that both had most of the water removed, plus I then added some antifreeze. Another advantage of doing this is you can tell if the plugs have any leaks as they bubble under water. I had a problem with the one and it kept leaking a small stream of bubbles, until I replaced the rubber gasket.
With the pool completely full, it won't have more than 1/2" of water or so on the cover as it builds up enough to overflow the side track. My thought process was that experience has shown that the water level INSIDE the pool will always be at the same level as the water on top of the cover when you have a water proof cover. This is because the water on top of the cover will displace the same amount of water inside the pool, so unless you're very religious about pumping it off the cover, you WILL get water inside the skimmer if you only drain it down just below the bottom of the inlet.
I learned this last summer after a very hard rain that left about 4" of water on the cover, which was all it could hold anymore. I opened the cover slightly, and noted that the water inside the pool was also right at the edge of overflowing. When I thought about it, it made sense, as the cover doesn't do anything other then separate the water inside and outside the pool, and other than the slight buoyancy of the cover, the two water levels will be the same, particularly around the edges of the pool. Therefore, if you only drain it to just below the skimmer and don't do anything to protect it, you have to be very consistent to keep the water pumped off or it will come up enough to put water back into the skimmer.