Ask Lemmygrad

https://en.wikipedia.org/wiki/Mpemba_effect

I would say the science on this doesn't seem very solid.

Yeah you can point to convection in the warmer liquid making heat transfer more efficient, to evaporation reducing the total amount of liquid, or to the fact that formation of ice isn't solely tied to temperature falling below zero, and you can - under specific circumstances in which the conditions for the formation of the initial seed crystals are not ideal - have water below the freezing point but not yet frozen, but i think these are marginal effects at a large enough scale.

For practical purposes i would say it depends on what size the volume of water is, how much warmer the warm water is, and how cold it is outside (plus maybe some secondary factors like what kind of container it is in - closed, open, good thermal conductivity, bad, lots of surface area, etc.). Obviously if there is a big difference in temperature between the two volumes, the amount of thermal energy in the warmer water will be so much higher that even allowing for the possibility of some effects leading to more efficient energy transfer away from the warmer volume, you'll still have the cold one freeze first.

I mean, the most simplified way to think about it is this: the warm water needs to first reach the temperature of the cold water before it can go to freezing. But by the time it does that the cold water will have already cooled down even lower. The formerly warm will now be in the same state as the cold water was initially, but the cold water has a head start. How can the warmer ever catch up if the rate of cooling depends only on the temperature differential between the liquid and the outside?

Of course this is an idealized model and in the real world you will have secondary effects (such as the evaporation i mentioned earlier - for instance if the temperature outside is just below zero and not some crazy low negative temperature, then maybe there is enough time for the evaporation of the warmer volume to make a difference), but can those make a big enough difference in your specific use case? I would suggest you just do the experiment yourself. Put two identical buckets of water out in winter when the temperature outside is below freezing, one with hot water one with cold, and see which one freezes first. My money is on the cold one, but trying it out is the only way to know for sure right?