Not to get into the discussion about whether spins should be part of the Private Pilot PTS or not, but rather to answer the original question...
I did not do "spin training" specifically as part of my CFI prep. I had done aerobatic training and had owned a Pitts Special before ever deciding to work on my instructor certificate, so the training I had was taken from a different viewpoint with a different goal in mind. However, I never got the logbook endorsement specifically related to spins for an instructor certificate, so when I was working on the CFI I needed to demonstrate spins so I could get the endorsement. Here's where the fun began!
I was taking my CFI prep training at Daytona Beach (a good excuse for a winter "vacation" while still accomplishing something). The only thing the flight school had that was spinnable was a very tired Cessna 150. So here we went, me (and I'm no small guy) and the instructor I was working with (not huge but not small either) in the 150 on a day that was about 85 degrees and about 80% humidity. True, we started out basically at sea level, but still, the 150 was not at all interested in climbing with any great alacrity.
By the time we were high enough to do the first spin we were already, hot, tired, and quite frankly, bored. So we did the first spin. It was a normal spin but of course quite fun (as spins are) so we decided we'd do another one. Some more climbing and we were ready for the next spin. Another fun time and again the decision that it was not enough, so one more was in order. More climbing! (At least the 150 was getting a bit lighter as we burned off fuel in the climbs.) We finally were high enough again to do one more, and we did an extra turn just for the heck of it. We then decided that we didn't have enough fuel to do one more so we headed back.
The moral of story is that.... Well, there really isn't any moral. Just the lesson that density altitude can have an effect even at sea level!
Cheers!
Joe