did you say very cold? How cold it is? -20F?
there are several possibilities. Some very likely another one not so much, but still possible.
Start from last one
First - thermostat is not working, replace it and it should be fine. BTW - you may drain and/or flush radiator also since antifreeze will have to be drained.
Second - if it is really cold and your antifreeze is not very good it could freeze in radiator. When you start engine it overheats almost right away it could be it because frozen fluid is solid and does not flow
Third (which just came to my mind) - water pump. Sometimes it runs out and has to be replaced.
Fourth - not enough of fluid - add some and see what happens.
Now, how to find it out....
Open the hood, check the coolant reservoir for fluid. Is it liquid? If so, is it above minimum?
If so, two options are excluded.
Then, start the car. Localize two thick rubber pipes - one delivering coolant to radiator, another below radiator to engine. The upper one should be hot first, the bottom one gets hot after the radiator is hot.
So, start engine and keep touching all the pipes. If you can feel heat on some of them (also, the small ones going to the heater core) its fine. If you can get plenty of heat from heater - water pump is fine.
If the engine reaches its right temp you should feel the thick upper pipe is getting hot. Then radiator is warming up and after several minutes bottom one will get hot too. After next few minutes the fan on radiator should start spinning.
Let me know what of this worked what not.
EDIT
there are also some issues with overheating when air/gas ratio is off.