Having empirically tested this, I can answer that yes, in my circumstances, hot water can freeze faster.
Some years ago, I kept chickens here in Michigan through the winter. I wanted to leave them with access to water while I was gone at work, but after filling the tank in the morning, I'd often come back to a block of ice and thirsty chickens in the evening. My experimental procedure was as follows: On a Saturday when I'd be home all day, I filled two identical 5 quart poultry waters to the same level, one with 115F hot tap water and one with normal 47F cold tap water. Both came from our well, from a sink with an aerator, and both passed through a softener. The hot water had been heated in a tank-style residential water heater, not over the stove. The troughs were left outside of the coop in a shed (several feet apart) to prevent unpredictable chicken activity from messing with the results. I put thermocouples in both troughs and checked in every half hour to take readings.
The hot water froze first by several hours!
The cold one reached 32F first, and after hitting 47F the rate of change of the one that had been hot was similar to the cold one (maybe slightly faster, but my measurements were too coarse to be confident of that), but both spent quite a bit of time at exactly 32F. The hot one just spent so much less time at 32F that the couple of hours to drop to 47F didn't matter. Both still had a considerable volume of liquid water in the bulk tank, the part exposed to air froze first, but that's still a failure because the chickens couldn't drink. I didn't have any equipment to measure dissolved gasses in the water, or measure convection or stacking in the tank, measure the rate of evaporative cooling, measure the rate of cold air being pulled over the surface by convection driven by the hot water temperature differential, or otherwise test any other factors that might be different from two apparently identical 32F tanks of water, all I knew is that the hot water froze faster.
The result of the experiment was just to put a small electric heating adapter under the base. After that it didn't matter. Another tragic example of pragmatism over curiosity...
Great experiment, and thanks for writing it up. I'd encourage you to get your 10 minutes of internet fame by reproducing the experiment next winter with pictures and measurements. I have to say, despite your experience, I'm still doubtful. Or rather, I'm still almost certain that there must be something besides the temperature that is causing the effect you saw.
For example, let's say you started with the hot water, and then let it cool to 47F--perhaps by putting it outside in below freezing weather. You then ran another tub of hot water, and did the experiment between those two. It definitely seems impossible to me that the new hot one would freeze first, which leads me to believe there must be something measurably different between the cool tap water version and the cooled down hot water.
Some years ago, I kept chickens here in Michigan through the winter. I wanted to leave them with access to water while I was gone at work, but after filling the tank in the morning, I'd often come back to a block of ice and thirsty chickens in the evening. My experimental procedure was as follows: On a Saturday when I'd be home all day, I filled two identical 5 quart poultry waters to the same level, one with 115F hot tap water and one with normal 47F cold tap water. Both came from our well, from a sink with an aerator, and both passed through a softener. The hot water had been heated in a tank-style residential water heater, not over the stove. The troughs were left outside of the coop in a shed (several feet apart) to prevent unpredictable chicken activity from messing with the results. I put thermocouples in both troughs and checked in every half hour to take readings.
The hot water froze first by several hours!
The cold one reached 32F first, and after hitting 47F the rate of change of the one that had been hot was similar to the cold one (maybe slightly faster, but my measurements were too coarse to be confident of that), but both spent quite a bit of time at exactly 32F. The hot one just spent so much less time at 32F that the couple of hours to drop to 47F didn't matter. Both still had a considerable volume of liquid water in the bulk tank, the part exposed to air froze first, but that's still a failure because the chickens couldn't drink. I didn't have any equipment to measure dissolved gasses in the water, or measure convection or stacking in the tank, measure the rate of evaporative cooling, measure the rate of cold air being pulled over the surface by convection driven by the hot water temperature differential, or otherwise test any other factors that might be different from two apparently identical 32F tanks of water, all I knew is that the hot water froze faster.
The result of the experiment was just to put a small electric heating adapter under the base. After that it didn't matter. Another tragic example of pragmatism over curiosity...