I used a new plug last year on a 17 year old skimmer and it leaked. (Just drips but still took no time to fill the skimmer). In hindsight of reading of them leaking for years, and all the terrible reviews online, when I had my own it was clear as day. The skimmer was out of square from years of UV exposure. The plug was most certainly square and even with the thick rubber gasket it was too much to overcome. So I jam packed the skimmer with cut up noods. There was maybe a half gallon of available space left, and none of it could freeze and expand with any force.
You worry isn’t even that the skimmer will freeze solid. In grounds do it all the time and the ice expands upwards. But in an above ground pool you worry about the ice in the pool being firmly attached to the skimmer and taking the wall with it when it shifts as it starts to melt. Much harder to do with an inground wall.
You can do either. If you drain below the skimmer, leave the pipe open so any non frozen water can drain if/when it gets that high. Consider a way for runoff if that happens because you don’t want the falling water to erode the outside of the wall area. Some pavers or a ramp of some kind to get the water away will both work fine.
If you leave the water high, plug the pipe and stuff the skimmer with noods.