EDIT: found it based on SCHiM's comment: http://flo2s.com/floating/what-is-a-float-tank/
You do feel the water, at least a bit. It might have been a little on the cold side, which didn't help the experience. I wasn't freezing to death or anything, but by the end was thinking, "Yeah, this could be half a degree warmer."
I didn't experience anything special. I meditate and whatnot and am pretty comfortable in the company of my own mind, so it was kind of like a long meditation session, though I never got in really deep. I was too busy watching myself for any novel reactions, I guess.
It lasted for an hour or ninety minutes and was pretty boring. My girlfriend reported a similar experience. YMMV, and you should try it and find out. It wasn't unpleasant, there just wasn't much there there (which is likely a commentary on the sterility of my mental environment or something.)
I believe some frogs do have such receptors: http://booksandjournals.brillonline.com/content/journals/10....
In my experience if you put your hand in water with similar temperature to your hand it's hard to notice if there is any water there or you are just still touching air. You have to rule out other senses to make this work.