I've gotten water as far as the galvanized pipe out to the carriage house -- but that galvanized has a hole in it in a very inconvenient spot -- right under here:
I can cut an access from inside the little cabinet under those stairs, which won't be too much of a pain, but my Dad had a good idea. The pipe coming up in the carriage house (i.e. the pipe that's been buried in the back yard) is black PVC pipe, so there's a junction between the galvanized and that black pipe somewhere. If the galvanized section is straight, we might be able to dig up the junction, unhook it, then pull the entire galvanized section out, repair it, and put it back.
So tomorrow, I'll try getting to the break in situ, but if I fail, then Tuesday we'll try Dad's idea. And if that fails, I guess we'll just lay a new section of pipe through the same place or something.
One little gripe. This section is in the "crawl" (which is about five inches high) under the back rooms -- that has a grate open to the outside. So again: it was really, really not surprising that pipes in this area might freeze. You just have to wonder what people are thinking.