This is kind of a rough calc because I found close to no "extra information" about it.
The chars take around a second to be frozen. So, that's the time.
Let's say the temperature is room temperature. 23 Celsius.
The character being frozen is Jacque Briggs, let's say she is 50 kilograms.
Lowball: For someone to get frostbite, the temperature has to go down to -4 Celsius. 23+4 = 27.
The formula is: E=m*c*ΔT
I get: 4,725,000 joules or, 1.129 kilograms of TNT.
That is the energy required to freeze someone alive... but without taking into account the time, so the value must be far higher considering they freeze in one second.
DontTalk's fixed version
Heat change = 37°C - (-4°C) = 41°C
E1 = 50kg * 3500 J/kg*K *41°C = 7175000J
So 25kg = 25000g water.
Enthalpy of fusion of water = 333.55 J/g
E2 = 25000g * 333.55 J/g = 8338750 J
So total energy = 7175000J + 8338750J = 1.551375e7J
It should be noted that 50kg human female is a low end.
To do an average:
Average human weight = 62kg
So water mass = 0.65*62kg.
So total energy = 62 * 3500 * 41 + 0.65*62*1000*333.55 = 2.2339065e7 J