The radiator is always froze up too

Reverse flush the system, drain, and refill with a 50/50 solution of the proper antifreeze and distilled water. This is the ideal time to replace the thermostat, if you sense if may be corroded and sticking closed. Replace the radiator, if phosphate scale has blocked passages in the radiator.

Is that why the radiator is always froze?

The radiator and engine block will freeze, if the amount of antifreeze in the coolant is too low for the temperatures in your area. Freezing can destroy the engine block and cooling system.