Funny thing about that. The "squeaky clean" feeling you get when you shower with hard water is actually from the hard water preventing all the soap from rinsing off your skin. The "slimy" feeling from showering in soft water is the actual feel of your hair and skin when wet after all of the soap is rinsed out.
I have a really hard time when I go on vacation and have to shower somewhere with hard water. My skin gets really dry from the residue left on it and it will crack and peel. My scalp is affected the same way and will itch and sting and scab. It also makes my hair really dry and brittle and tangle-y.