Inside a 70 degree F kitchen or outside in the winter at 0 F on a propane burner? Assume a rolling, 212 F boil and the same number of BTUs. Will it make any difference whatsoever?
Outside, because the wind will carry away more mass, lowering the partial pressure of the water vapor in the boundary layer above the pot, allowing more water to vaporize. With no wind, it would still be where it was colder, because there would be more natural convection.
Off the top of my head, I see three effects: Outside, the wind carries away steam near the pot, so less vapor pressure, makes it evaporate easier. And, the dry cold air has a lower vapor pressure anyway, so even without the wind, it will evaporate easier outside.
But the pot is losing lots more heat to the cold outside, so a burner that just gets the water boiling outside will have the water at a much harder boil inside, therefore water will evaporate away more quickly inside.
I suspect that the second effect dominates, and – assuming the same BTU input – the water will boil away faster inside. Now if you’re trying to keep the same level of boil inside and outside, I think the outside one will evaporate faster, but using a higher burner than the inside one.
Assuming the same rolling boil in both places, and that “rain” is not condensing from the steam and falling back into the pot the both pots should boil dry simultaneously.
the pot indoors would lose more water due to the more violent boil.