Unless you were in a dry suit, I don't know how you do it. The local quarry, which I dove a few years back, is quite deep, and tends to run around 45 degrees in the bottom. I've dove it in a 5 mm full wetsuit and gloves, 7 mm hood and boots. Even so, I was very aware the water around me was scary cold, and I was okay (not really shivering) but mindful (I imagine the 2nd thermocline to get to this cold layer might've been 60 feet deep or so).
But the idea of going in water that's cold like that at the surface? Ugh! Is that what you guys did? I can go in when the top layer's upper 70's or 80-ish (which fills my wetsuit with warm water), the middle layer's probably in the 60's (guessing), and then finally deep down, bitterly cold water doesn't flood me all at once.
Talking about miserably cold water is making Cozumel's tropical 'bath water' sound wonderful!