It depends on how the spell really works.

From your description I get two possible situations:

1. Target is frozen to 1K instantly AND covered with thick ice at the same temperature.

2. Target is not frozen, but instantly covered with thick ice at 1K.

The scenarios are quite different.

In the first case the target is with most probability destroyed (barring some counter magic): at 1K the crew would die instantly, all electronics will be shattered by thermal stresses and even the component materials (even most metals) would become so brittle they will shatter easily (maybe also from the sheer weight of the tank). Moreover most chemical reactions will effectively stop.

In the second case, it depends heavily on the thermal shielding of the tank and the total mass of the ice produced. The 1K ice will begin drawing thermal energy from the environment (outer side) and from the tank (inner side), rising its temperature and lowering the tank temperature in the process. This process continues until the tank, the ice and the external environment reach thermal equilibrium. It's quite a difficult calculation to perform without knowing the actual construction of the tank, but in the end, it depends on the relative thermal capacities of the mass of ice and of the tank.

If there is enough ice to bring down the temperature of the tank to dangerous level (for the materials and/or crew), then it would be an effective spell.

Keep in mind that the freezing effect will cool down the tank from outside, so before the thermal equilibrium is reached, the outer tank parts will be cooled faster, so the first parts affected are the outer joints (e.g the joints between tracks elements, for example), which could become stuck due to thermal shrinkage, and maybe break if the tank was moving.

To put some numbers in: the specific heat for ice is about 2.1 kJ/(kg K), whereas that of steel is about 0.42 kJ/(kg K). The specific heat means how much energy is needed per kilogram to raise the temperature of the material by 1K. So assuming the tank has a mass of 10t = 10000kg and it can resist up to -30°C and the ambient temperature is 20°C, you need to lower its temperature by 50K.

This requires 0.42 * 10000 * 50=210MJ of energy to be transferred to the ice. Assuming the mass of ice is 1000kg, for it to reach -30°C (243K) it would take a temperature increase of 242K, so the energy required is: 2.1 * 1000 * 242=508MJ.

So yes, 1000kg of ice would be sufficient to make 10t of steel to go below -30°C. The problem is that this is at thermal equilibrium and doesn't take into account the time needed and any sort of thermal insulation or heating system the tank could have. Moreover there is also the heat exchanged with the environment (part of the ice will increase its temperature drawing heat from the atmosphere instead of from the tank).

It depends on how the spell really works.

From your description I get two possible situations:

1. Target is frozen to 1K instantly AND covered with thick ice at the same temperature.

2. Target is not frozen, but instantly covered with thick ice at 1K.

The scenarios are quite different.

In the first case the target is with most probability destroyed (barring some counter magic): at 1K the crew would die instantly, all electronics will be shattered by thermal stresses and even the component materials (even most metals) would become so brittle they will shatter easily (maybe also from the sheer weight of the tank). Moreover most chemical reactions will effectively stop.

In the second case, it depends heavily on the thermal shielding of the tank and the total mass of the ice produced. The 1K ice will begin drawing thermal energy from the environment (outer side) and from the tank (inner side), rising its temperature and lowering the tank temperature in the process. This process continues until the tank, the ice and the external environment reach thermal equilibrium. It's quite a difficult calculation to perform without knowing the actual construction of the tank, but in the end, it depends on the relative thermal capacities of the mass of ice and of the tank.

If there is enough ice to bring down the temperature of the tank to dangerous level (for the materials and/or crew), then it would be an effective spell.

Keep in mind that the freezing effect will cool down the tank from outside, so before the thermal equilibrium is reached, the outer tank parts will be cooled faster, so the first parts affected are the outer joints (e.g the joints between tracks elements, for example), which could become stuck due to thermal shrinkage, and maybe break if the tank was moving.

To put some numbers in: the specific heat for ice is about 2.1 kJ/(kg K), whereas that of steel is about 0.42 kJ/(kg K). The specific heat means how much energy is needed per kilogram to raise the temperature of the material by 1K. So assuming the tank has a mass of 10t = 10000kg and it can resist up to -30°C and the ambient temperature is 20°C, you need to lower its temperature by 50K.

This requires 0.42 * 10000 * 50=210MJ of energy to be transferred to the ice. Assuming the mass of ice is 1000kg, for it to reach -30°C (243K) it would take a temperature increase of 242K, so the energy required is: 2.1 * 1000 * 242=508MJ.

So yes, 1000kg of ice would be sufficient to make 10t of steel to go below -30°C. The problem is that this is at thermal equilibrium and doesn't take into account the time needed and any sort of thermal insulation or heating system the tank could have. 

Moreover there is also the heat exchanged with the environment (part of the ice will increase its temperature drawing heat from the atmosphere instead of from the tank).

Keep also in mind that ice is a good thermal insulator (think igloos) so the inner layer of ice will slow down heat transfer from the outside layers. So covering an object in super-cool ice is not an efficient strategy to cool it down quickly (it would be much more efficient to expose the tank to a freezing wind).

In the end, it would require quite a lot of ice to cool it down, and it won't be quick. Most probably, once you burden the tank with some additional tons of ice, it will stop in its tracks just for the sheer weight of the ice.

It depends on how the spell really works.

From your description I get two possible situations:

1. Target is frozen to 1K instantly AND covered with thick ice at the same temperature.

2. Target is not frozen, but instantly covered with thick ice at 1K.

The scenarios are quite different.

In the first case the target is with most probability destroyed (barring some counter magic): at 1K the crew would die instantly, all electronics will be shattered by thermal stresses and even the component materials (even most metals) would become so brittle they will shatter easily (maybe also from the sheer weight of the tank). Moreover most chemical reactions will effectively stop.

In the second case, it depends heavily on the thermal shielding of the tank and the total mass of the ice produced. The 1K ice will begin drawing thermal energy from the environment (outer side) and from the tank (inner side), rising its temperature and lowering the tank temperature in the process. This process continues until the tank, the ice and the external environment reach thermal equilibrium. It's quite a difficult calculation to perform without knowing the actual construction of the tank, but in the end, it depends on the relative thermal capacities of the mass of ice and of the tank.

If there is enough ice to bring down the temperature of the tank to dangerous level (for the materials and/or crew), then it would be an effective spell.

Keep in mind that the freezing effect will cool down the tank from outside, so before the thermal equilibrium is reached, the outer tank parts will be cooled faster, so the first parts affected are the outer joints (e.g the joints between tracks elements, for example), which could become stuck due to thermal shrinkage, and maybe break if the tank was moving.

It depends on how the spell really works.

From your description I get two possible situations:

1. Target is frozen to 1K instantly AND covered with thick ice at the same temperature.

2. Target is not frozen, but instantly covered with thick ice at 1K.

The scenarios are quite different.

In the first case the target is with most probability destroyed (barring some counter magic): at 1K the crew would die instantly, all electronics will be shattered by thermal stresses and even the component materials (even most metals) would become so brittle they will shatter easily (maybe also from the sheer weight of the tank). Moreover most chemical reactions will effectively stop.

In the second case, it depends heavily on the thermal shielding of the tank and the total mass of the ice produced. The 1K ice will begin drawing thermal energy from the environment (outer side) and from the tank (inner side), rising its temperature and lowering the tank temperature in the process. This process continues until the tank, the ice and the external environment reach thermal equilibrium. It's quite a difficult calculation to perform without knowing the actual construction of the tank, but in the end, it depends on the relative thermal capacities of the mass of ice and of the tank.

If there is enough ice to bring down the temperature of the tank to dangerous level (for the materials and/or crew), then it would be an effective spell.

Keep in mind that the freezing effect will cool down the tank from outside, so before the thermal equilibrium is reached, the outer tank parts will be cooled faster, so the first parts affected are the outer joints (e.g the joints between tracks elements, for example), which could become stuck due to thermal shrinkage, and maybe break if the tank was moving.

To put some numbers in: the specific heat for ice is about 2.1 kJ/(kg K), whereas that of steel is about 0.42 kJ/(kg K). The specific heat means how much energy is needed per kilogram to raise the temperature of the material by 1K. So assuming the tank has a mass of 10t = 10000kg and it can resist up to -30°C and the ambient temperature is 20°C, you need to lower its temperature by 50K.

This requires 0.42 * 10000 * 50=210MJ of energy to be transferred to the ice. Assuming the mass of ice is 1000kg, for it to reach -30°C (243K) it would take a temperature increase of 242K, so the energy required is: 2.1 * 1000 * 242=508MJ.

So yes, 1000kg of ice would be sufficient to make 10t of steel to go below -30°C. The problem is that this is at thermal equilibrium and doesn't take into account the time needed and any sort of thermal insulation or heating system the tank could have. Moreover there is also the heat exchanged with the environment (part of the ice will increase its temperature drawing heat from the atmosphere instead of from the tank).