Interesting -- most water softener setups I have seen are only plumbed into the hot water, I've been told that this is because drinking softened water is not recommended.
Hum. This is the first house I've ever owned, and this is the 3rd or 4th thing I've been told wasn't "normal" about it. The previous owner also ran a construction company, and I'm pretty sure he did a lot of work on this house himself, so it wouldn't surprise me if this is another instance of that.
For the most part, though, everything works well enough. So I'm happy overall.