The thermal conductivity of water is 0.591, the thermal conductivity of air is 0.024. So completely ignoring wind, convection, radiation, sweating and so on you lose ~30× more heat in water than air. Round that down a bit to account for sweat and the other factors and you're probably still burning multiple times more calories simply by standing in a cold pool compared to cold air (at the same temperature).
If you get too hot, you start burning calories again in order to pump blood and lose heat. In this case you burn more calories in air as the cooling is less efficient.
So, if you want to burn calories here's the summary: if you're ice fishing in Norway and there's a 0° pool and 0° air then jump in the pool. If you're in Majorca and it's 35° outside and you're a sweaty mess, stay out of the nice cool 25° pool. If you're in Abu Dhabi and you have a choice between a 50° pool or 50° air, then jump on in you big lobster. Basically aside from baths and saunas and whatnot it's the unpleasant option that burns the calories.
The thermal conductivity of water is 0.591, the thermal conductivity of air is 0.024. So completely ignoring wind, convection, radiation, sweating and so on you lose ~30× more heat in water than air. Round that down a bit to account for sweat and the other factors and you're probably still burning multiple times more calories simply by standing in a cold pool compared to cold air (at the same temperature).
If you get too hot, you start burning calories again in order to pump blood and lose heat. In this case you burn more calories in air as the cooling is less efficient.
So, if you want to burn calories here's the summary: if you're ice fishing in Norway and there's a 0° pool and 0° air then jump in the pool. If you're in Majorca and it's 35° outside and you're a sweaty mess, stay out of the nice cool 25° pool. If you're in Abu Dhabi and you have a choice between a 50° pool or 50° air, then jump on in you big lobster. Basically aside from baths and saunas and whatnot it's the unpleasant option that burns the calories.