You do not want to have water in those pipes or in the skimmer body itself (unless you have a gizmo or similar item in there)..
On your suction side you use either a plate or gizmo on the skimmer, and leave the valve on the suction side open. Or drain below the skimmer and leave the valve open.
On your return, you put a loop in there for some reason - that loop is going to hold water (it also adds head loss and reduces your flow rate). You are going to have to blow out that line and I would put some antifreeze in it. You can put a plug in your return.
You *could* put a T in the bottom run of that loop, with the T pointing down, and a valve on the end of the T. Then you would have a drain in the lowest part of your return line. The it would be self draining, and there would be no need for blowing out that line, or adding antifreeze.
This is my set up
You cannot see where it enters the skimmer and return but it is a straight run. It goes from the ground level pipe, up to the skimmer and return.
You can see that my unions are at the lowest point in the runs (they are on the filter side, right after the valves). I use a plate on my skimmer and a rubber plug on my return. I would like to use a threaded plug on the return, but I have an aqualiminator, and that does not take threaded plugs. Once I plug the skimmer and return, I remove the filter at the unions and open the valves. The pipes drain on their own, and nothing will collect in them. I leave the valves open, just in case something happens (rain/snow will collect in the skimmer and this lets it drain, and once it froze deep enough to pull the plug on the return, so the pool drained down to the return, which was better than having it fill the pipe, freeze, crack the pipe, and then drain anyway)
I do zip tie some hardware cloth over the ends of the pipes, just so nothing builds a nest up in there (we have chipmunks and other such critters around here)
-dave