The temperature of your cold water will depend on where you live too. In Florida the groundwater is 70 degrees. I live in the mountains at 7000 feet, the water is much colder.

I find that whenever I'm coming down with some kind of illness or am overly tired my ability to cope with cold showers drops through the floor and my body lets me know this ain't acceptable. Maybe that was it? Or could just be you have lower cold tolerance? Uncontrollable shivering is probably best avoided though!

Get into a proper Finnish sauna at around 95 degrees Celsius. After ten to fifteen minutes you will long for the cold shower. And it will actually feel good.