FWIW, we have hard water in our home. On the hardness scale it is an 8 and is 5ppm iron. Straight from the well, the water has a sulphur smell and leaves rust stains on everything. Our 22-year-old water softener died a month ago and the job it did in eliminating rust stains and smell was pretty good. We still got some minimal rust stains, but not much (you could really tell on the shower curtains). For me and my family the taste is horrible without the softener, and bad with the softener (hello 5 gallon RO water jugs for drinking). I just replaced the softener 5 days ago and the difference is immense. We use our 'softened' water for everything except drinking as we like the RO water for that. I've never really tasted 'salt' in the water excepting for a handful of times.
With that said, I would not use our unfiltered water for kit wine making. Taste (and iron) is the concern. I do not use 'softened' water for kit wine making as I've read that there are adverse effects on the wine using well treated water. I use store bought spring water. Now that I type this, I may just try an experiment with Vintners best or a WE Classic comparing softened water to store bought spring water, just to find if I can detect a difference, but my head says to just stick with spring water as I have had success with it. Maybe someday I will play around with it. Now, municipal treated water (city water) is something I've used too, but only on a couple of batches and I've not detected anything really strange about it...other than everyone saying not to use it, and I don't have it anyway.