Good neat job. I agree with closing the ends of the tubes. They will collect wasps nests when left open.
You may still have water get in the tubes. When welding tubing closed, the heated air will build up pressure and, on the last weld, will blow a small hole in the melted steel weld. At least that has been my experience when welding galvanized pipe gates. I think you can let the assembly cool and tack weld the hole closed if desired.