It sounds like a contradiction but it happens. Your car froze up and it is overheating like it is the middle of August. What can cause a car’s engine to freeze up and overheat at the same time?
The short answer is that a lack of anti-freeze has resulted in the contents of the cooling system freezing up inside the car’s engine--in the radiator or the hoses that carry the anti-freeze from the radiator to the engine and back again. Insufficient cold weather protection is caused by an improper concentration of coolant/anti-freeze. This can happen when other work is done to the cooling system, possibly a hose replacement, and when the system is topped off with water, which compromises the strength of the anti-freeze. Another possibility is that someone has confused pre-mixed anti-freeze with the full strength version and further diluted the 50/50 mix with additional water.
But enough of pointing fingers, what do you do now?
Don't run the vehicle. You might think that as the engine heats up the freeze point will break loose. What happens instead is that the radiator blows apart as extreme pressure builds up due to the coolant’s inability to circulate. No, what you have to do is seek shelter from the cold.
Try a little warming. When you have moved the vehicle out of the cold and to a warm area, it would be best just to let the engine thaw out at its own rate, but that usually is not quickly enough. So you might move a space heater (avoiding anything that could cause a fire) as close to the engine as possible to accelerate the thawing process. After the car has been out of the cold for some time you can try starting it, monitoring the temperature gauge to make sure that the ice blockage has melted. Be sure to stay with the car as it is running since overheating can occur very rapidly.
Drain and refill the radiator. Once you have confirmed that the ice is gone, drain and refill the radiator to the proper concentration of anti-freeze, making sure that you run the vehicle long enough for the thermostat to open and then adding more anti-freeze.
Check your levels before winter hits. Having an engine freeze up is something that usually only happens once in a lifetime of driving, because the lesson learned is forever seared into one’s memory. The way to avoid the trauma is to have the anti-freeze strength checked at the beginning of each winter driving season. It is a job you can do yourself with a very low degree of difficulty and a minimal investment of less than $10, which is the price of a tester.
An engine overheating during freezing weather is one instance when you should assume the worst which is that the motor has frozen up, because the consequences of assuming anything less are far too consequential.