Welcome to Just Answer. I will do my best to fully answer your question(s).
Yes that should do it once you close the supply valves and open up the outdoor faucet to release pressure the water should drain down out of the exterior piping.
HOWEVER, if you have any piping that goes to the exterior faucet that creates a trap then that water will not drain out completely. A trap is created when water supply piping rises vertically, turns horizontally, then turns vertically DOWNWARDS before heading in a horizontal direction, once again. If you have this situation with your piping in the wall supplying the faucet then you need to remove that as well. This arrangement is common practice when piping needs to get around an obstacle in a wall and cannot be plumbed in any other matter.
OK, a little confused...in the fall I do shutoff the inside hot and cold pipes to the outside shower, then open the outdoor shower valve. This does not seem to work as the plastic internal facet parts located outside are split come the spring. I think I need to get the water out of this outside facet?
I am confirming that the solution you suggest (installing drain valves at the elbows in the basement will drain out the water) IF there is no water that can be trapped in the piping. It will only get trapped IF the situation I listed in my earlier post is present in the water supply piping rising up to the faucet.
If the piping goes only vertically up and directly into the faucet then all water will drain out just fine.
ok, got it. I bought 2 drains, they look like a standard outside water facets. The two copper pipes comes down in an "L" like shape. Any tips/tricks in cutting the pipes and soldering? Which way should the valves face? Where should I cut the pipe? (at the elbow or just above/below?)
so on the "L", put the drain on the horizontal, (bottom part of the "L)? And then which way to face the drain?