You are in luck (sort of). The two brass pieces in the first photo are known as "Shark Bite" fittings. They will slip off the short length of white plastic pipe between them, and you can replace the pipe and slip the fittings back on. You need a special "key" to release the fittings, and assuming you don't have one, you can buy one for a couple bucks at Home Depot, etc.
It appears that a previous owner had the same problem (freezing) with the original plumbing, and repaired it using the Shark Bite fittings. Draining this bit of plumbing - the outside shower - is one step in the winterizing procedure that you will find discussed here on the Forum.
Bill
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